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To provide high torques needed to move a robot’s links, electric actuators are followed by a transmission system with a high transmission rate. For instance, gear ratios of 100:1 are often used in the joints of a robotic manipulator. This results into an actuator with large mechanical impedance (also known as nonback-drivable actuator). This in turn generates high contact forces when collision of the robotic mechanism occur and can cause humans’ injury. Another disadvantage of electric actuators is that they can exhibit overheating when constant torques have to be provided. Comparing to electric actuators, pneumatic actuators have promising properties for robotic applications, due to their low weight, simple mechanical design, low cost and good power-to-weight ratio. Electropneumatically actuated robots usually have better friction properties. Moreover, because of low mechanical impedance, pneumatic robots can provide moderate interaction forces which is important for robotic surgery and rehabilitation tasks. Pneumatic actuators are also well suited for exoskeleton robots. Actuation in exoskeletons should have a fast and accurate response. While electric motors come against high mechanical impedance and the risk of causing injuries, pneumatic actuators exhibit forces and torques which stay within moderate variation ranges. Besides, unlike direct current electric motors, pneumatic actuators have an improved weight-to-power ratio and avoid overheating problems.

The aim of this paper is to analyze a nonlinear optimal control method for electropneumatically actuated robots. A two-link robotic exoskeleton with electropneumatic actuators is considered as a case study. The associated nonlinear and multivariable state-space model is formulated and its differential flatness properties are proven. The dynamic model of the electropneumatic robot is linearized at each sampling instance with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. Within each sampling period, the time-varying linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. An H-infinity controller is designed for the linearized model of the robot aiming at solving the related optimal control problem under model uncertainties and external perturbations. An algebraic Riccati equation is solved at each time-step of the control method to obtain the stabilizing feedback gains of the H-infinity controller. Through Lyapunov stability analysis, it is proven that the robot’s control scheme satisfies the H-infinity tracking performance conditions which indicate the robustness properties of the control method. Moreover, global asymptotic stability is proven for the control loop. The method achieves fast convergence of the robot’s state variables to the associated reference trajectories, and despite strong nonlinearities in the robot’s dynamics, it keeps moderate the variations of the control inputs.

In this paper, a novel solution has been proposed for the nonlinear optimal control problem of robotic exoskeletons with electropneumatic actuators. As a case study, the dynamic model of a two-link lower-limb robotic exoskeleton with electropneumatic actuators has been considered. The dynamic model of this robotic system undergoes first approximate linearization at each iteration of the control algorithm around a temporary operating point. Within each sampling period, this linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. The linearization process relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. The modeling error which is due to the truncation of higher-order terms from the Taylor series is considered to be a perturbation which is asymptotically compensated by the robustness of the control algorithm. To stabilize the dynamics of the electropneumatically actuated robot and to achieve precise tracking of reference setpoints, an H-infinity (optimal) feedback controller is designed. Actually, the proposed H-infinity controller for the model of the two-link electropneumatically actuated exoskeleton achieves the solution of the associated optimal control problem under model uncertainty and external disturbances. This controller implements a min-max differential game taking place between: (i) the control inputs which try to minimize a cost function which comprises a quadratic term of the state vector’s tracking error and (ii) the model uncertainty and perturbation inputs which try to maximize this cost function. To select the stabilizing feedback gains of this H-infinity controller, an algebraic Riccati equation is being repetitively solved at each time-step of the control method. The global stability properties of the H-infinity control scheme are proven through Lyapunov analysis.

Pneumatic actuators are characterized by high nonlinearities which are due to air compressibility, thermodynamics and valves behavior and thus pneumatic robots require elaborated nonlinear control schemes to ensure their fast and precise positioning. Among the control methods which have been applied to pneumatic robots, one can distinguish differential geometric approaches (Lie algebra-based control, differential flatness theory-based control, nonlinear model predictive control [NMPC], sliding-mode control, backstepping control and multiple models-based fuzzy control). Treating nonlinearities and fault tolerance issues in the control problem of robotic manipulators with electropneumatic actuators has been a nontrivial task.

The novelty of the proposed control method is outlined as follows: preceding results on the use of H-infinity control to nonlinear dynamical systems were limited to the case of affine-in-the-input systems with drift-only dynamics. These results considered that the control inputs gain matrix is not dependent on the values of the system’s state vector. Moreover, in these approaches the linearization was performed around points of the desirable trajectory, whereas in the present paper’s control method the linearization points are related with the value of the state vector at each sampling instance as well as with the last sampled value of the control inputs vector. The Riccati equation which has been proposed for computing the feedback gains of the controller is novel, so is the presented global stability proof through Lyapunov analysis. This paper’s scientific contribution is summarized as follows: (i) the presented nonlinear optimal control method has improved or equally satisfactory performance when compared against other nonlinear control schemes that one can consider for the dynamic model of robots with electropneumatic actuators (such as Lie algebra-based control, differential flatness theory-based control, nonlinear model-based predictive control, sliding-mode control and backstepping control), (ii) it achieves fast and accurate tracking of all reference setpoints, (iii) despite strong nonlinearities in the dynamic model of the robot, it keeps moderate the variations of the control inputs and (iv) unlike the aforementioned alternative control approaches, this paper’s method is the only one that achieves solution of the optimal control problem for electropneumatic robots.

The use of electropneumatic actuation in robots exhibits certain advantages. These can be the improved weight-to-power ratio, the lower mechanical impedance and the avoidance of overheating. At the same time, precise positioning and accurate execution of tasks by electropneumatic robots requires the application of elaborated nonlinear control methods. In this paper, a new nonlinear optimal control method has been developed for electropneumatically actuated robots and has been specifically applied to the dynamic model of a two-link robotic exoskeleton. The benefit from using this paper’s results in industrial and biomedical applications is apparent.

A comparison of the proposed nonlinear optimal (H-infinity) control method against other linear and nonlinear control schemes for electropneumatically actuated robots shows the following: (1) Unlike global linearization-based control approaches, such as Lie algebra-based control and differential flatness theory-based control, the optimal control approach does not rely on complicated transformations (diffeomorphisms) of the system’s state variables. Besides, the computed control inputs are applied directly on the initial nonlinear model of the electropneumatic robot and not on its linearized equivalent. The inverse transformations which are met in global linearization-based control are avoided and consequently one does not come against the related singularity problems. (2) Unlike model predictive control (MPC) and NMPC, the proposed control method is of proven global stability. It is known that MPC is a linear control approach that if applied to the nonlinear dynamics of the electropneumatic robot, the stability of the control loop will be lost. Besides, in NMPC the convergence of its iterative search for an optimum depends on initialization and parameter values selection and consequently the global stability of this control method cannot be always assured. (3) Unlike sliding-mode control and backstepping control, the proposed optimal control method does not require the state-space description of the system to be found in a specific form. About sliding-mode control, it is known that when the controlled system is not found in the input-output linearized form the definition of the sliding surface can be an intuitive procedure. About backstepping control, it is known that it cannot be directly applied to a dynamical system if the related state-space model is not found in the triangular (backstepping integral) form. (4) Unlike PID control, the proposed nonlinear optimal control method is of proven global stability, the selection of the controller’s parameters does not rely on a heuristic tuning procedure, and the stability of the control loop is assured in the case of changes of operating points. (5) Unlike multiple local models-based control, the nonlinear optimal control method uses only one linearization point and needs the solution of only one Riccati equation so as to compute the stabilizing feedback gains of the controller. Consequently, in terms of computation load the proposed control method for the electropneumatic actuator’s dynamics is much more efficient.

A distinctive feature of tilt-rotor UAVs is that they can be fully actuated, whereas in fixed-angle rotor UAVs (e.g. common-type quadrotors, octorotors, etc.), the associated dynamic model is characterized by underactuation. Because of the existence of more control inputs, in tilt-rotor UAVs, there is more flexibility in the solution of the associated nonlinear control problem. On the other side, the dynamic model of the tilt-rotor UAVs remains nonlinear and multivariable and this imposes difficulty in the drone's controller design. This paper aims to achieve simultaneously precise tracking of trajectories and minimization of energy dissipation by the UAV's rotors. To this end elaborated control methods have to be developed.

A solution of the nonlinear control problem of tilt-rotor UAVs is attempted using a novel nonlinear optimal control method. This method is characterized by computational simplicity, clear implementation stages and proven global stability properties. At the first stage, approximate linearization is performed on the dynamic model of the tilt-rotor UAV with the use of first-order Taylor series expansion and through the computation of the system's Jacobian matrices. This linearization process is carried out at each sampling instance, around a temporary operating point which is defined by the present value of the tilt-rotor UAV's state vector and by the last sampled value of the control inputs vector. At the second stage, an H-infinity stabilizing controller is designed for the approximately linearized model of the tilt-rotor UAV. To find the feedback gains of the controller, an algebraic Riccati equation is repetitively solved, at each time-step of the control method. Lyapunov stability analysis is used to prove the global stability properties of the control scheme. Moreover, the H-infinity Kalman filter is used as a robust observer so as to enable state estimation-based control. The paper's nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs. Finally, the nonlinear optimal control approach for UAVs with tilting rotors is compared against flatness-based control in successive loops, with the latter method to be also exhibiting satisfactory performance.

So far, nonlinear model predictive control (NMPC) methods have been of questionable performance in treating the nonlinear optimal control problem for tilt-rotor UAVs because NMPC's convergence to optimum depends often on the empirical selection of parameters while also lacking a global stability proof. In the present paper, a novel nonlinear optimal control method is proposed for solving the nonlinear optimal control problem of tilt rotor UAVs. Firstly, by following the assumption of small tilting angles, the state-space model of the UAV is formulated and conditions of differential flatness are given about it. Next, to implement the nonlinear optimal control method, the dynamic model of the tilt-rotor UAV undergoes approximate linearization at each sampling instance around a temporary operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. The linearization process is based on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. The modelling error, which is due to the truncation of higher-order terms from the Taylor series, is considered to be a perturbation that is asymptotically compensated by the robustness of the control scheme. For the linearized model of the UAV, an H-infinity stabilizing feedback controller is designed. To select the feedback gains of the H-infinity controller, an algebraic Riccati equation has to be repetitively solved at each time-step of the control method. The stability properties of the control scheme are analysed with the Lyapunov method.

There are no research limitations in the nonlinear optimal control method for tilt-rotor UAVs. The proposed nonlinear optimal control method achieves fast and accurate tracking of setpoints by all state variables of the tilt-rotor UAV under moderate variations of the control inputs. Compared to past approaches for treating the nonlinear optimal (H-infinity) control problem, the paper's approach is applicable also to dynamical systems which have a non-constant control inputs gain matrix. Furthermore, it uses a new Riccati equation to compute the controller's gains and follows a novel Lyapunov analysis to prove global stability for the control loop.

There are no practical implications in the application of the nonlinear optimal control method for tilt-rotor UAVs. On the contrary, the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state-dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems which can be transformed to the linear parameter varying (LPV) form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions. The stability properties of the Galerkin series expansion-based optimal control approaches are still unproven.

The proposed nonlinear optimal control method is suitable for using in various types of robots, including robotic manipulators and autonomous vehicles. By treating nonlinear control problems for complicated robotic systems, the proposed nonlinear optimal control method can have a positive impact towards economic development. So far the method has been used successfully in (1) industrial robotics: robotic manipulators and networked robotic systems. One can note applications to fully actuated robotic manipulators, redundant manipulators, underactuated manipulators, cranes and load handling systems, time-delayed robotic systems, closed kinematic chain manipulators, flexible-link manipulators and micromanipulators and (2) transportation systems: autonomous vehicles and mobile robots. Besides, one can note applications to two-wheel and unicycle-type vehicles, four-wheel drive vehicles, four-wheel steering vehicles, articulated vehicles, truck and trailer systems, unmanned aerial vehicles, unmanned surface vessels, autonomous underwater vessels and underactuated vessels.

The proposed nonlinear optimal control method is a novel and genuine result and is used for the first time in the dynamic model of tilt-rotor UAVs. The nonlinear optimal control approach exhibits advantages against other control schemes one could have considered for the tilt-rotor UAV dynamics. For instance, (1) compared to the global linearization-based control schemes (such as Lie algebra-based control or flatness-based control), it does not require complicated changes of state variables (diffeomorphisms) and transformation of the system's state-space description. Consequently, it also avoids inverse transformations which may come against singularity problems, (2) compared to NMPC, the proposed nonlinear optimal control method is of proven global stability and the convergence of its iterative search for an optimum does not depend on initialization and controller's parametrization, (3) compared to sliding-mode control and backstepping control the application of the nonlinear optimal control method is not constrained into dynamical systems of a specific state-space form. It is known that unless the controlled system is found in the input–output linearized form, the definition of the associated sliding surfaces is an empirical procedure. Besides, unless the controlled system is found in the backstepping integral (triangular) form, the application of backstepping control is not possible, (4) compared to PID control, the nonlinear optimal control method is of proven global stability and its performance is not dependent on heuristics-based selection of parameters of the controller and (5) compared to multiple-model-based optimal control, the nonlinear optimal control method requires the computation of only one linearization point and the solution of only one Riccati equation.

The purpose of this article is to treat the nonlinear optimal control problem in EV traction systems which are based on 5-phase induction motors. Five-phase permanent magnet synchronous motors and five-phase asynchronous induction motors (IMs) are among the types of multiphase motors one can consider for the traction system of electric vehicles (EVs). By distributing the required power in a large number of phases, the power load of each individual phase is reduced. The cumulative rates of power in multiphase machines can be raised without stressing the connected converters. Multiphase motors are also fault tolerant because such machines remain functional even if failures affect certain phases.

A novel nonlinear optimal control approach has been developed for five-phase IMs. The dynamic model of the five-phase IM undergoes approximate linearization using Taylor series expansion and the computation of the associated Jacobian matrices. The linearization takes place at each sampling instance. For the linearized model of the motor, an H-infinity feedback controller is designed. This controller achieves the solution of the optimal control problem under model uncertainty and disturbances.

To select the feedback gains of the nonlinear optimal (H-infinity) controller, an algebraic Riccati equation has to be solved repetitively at each time-step of the control method. The global stability properties of the control loop are demonstrated through Lyapunov analysis. Under moderate conditions, the global asymptotic stability properties of the control scheme are proven. The proposed nonlinear optimal control method achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs.

Comparing to other nonlinear control methods that one could have considered for five-phase IMs, the presented nonlinear optimal (H-infinity) control approach avoids complicated state-space model transformations, is of proven global stability and its use does not require the model of the motor to be brought into a specific state-space form. The nonlinear optimal control method has clear implementation stages and moderate computational effort.

In the transportation sector, there is progressive transition to EVs. The use of five-phase IMs in EVs exhibits specific advantages, by achieving a more balanced distribution of power in the multiple phases of the motor and by providing fault tolerance. The study’s nonlinear optimal control method for five-phase IMs enables high performance for such motors and their efficient use in the traction system of EVs.

Nonlinear optimal control for five-phase IMs supports the deployment of their use in EVs. Therefore, it contributes to the net-zero objective that aims at eliminating the emission of harmful exhaust gases coming from human activities. Most known manufacturers of vehicles have shifted to the production of all-electric cars. The study’s findings can optimize the traction system of EVs thus also contributing to the growth of the EV industry.

The proposed nonlinear optimal control method is novel comparing to past attempts for solving the optimal control problem for nonlinear dynamical systems. It uses a novel approach for selecting the linearization points and a new Riccati equation for computing the feedback gains of the controller. The nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state-dependent Riccati equations.

Because of the various advantages of reinforcement learning (RL) mentioned above, this study uses RL to train unmanned aerial vehicles to perform two tasks: target search and cooperative obstacle avoidance.

This study draws inspiration from the recurrent state-space model and recurrent models (RPM) to propose a simpler yet highly effective model called the unmanned aerial vehicles prediction model (UAVPM). The main objective is to assist in training the UAV representation model with a recurrent neural network, using the soft actor-critic algorithm.

This study proposes a generalized actor-critic framework consisting of three modules: representation, policy and value. This architecture serves as the foundation for training UAVPM. This study proposes the UAVPM, which is designed to aid in training the recurrent representation using the transition model, reward recovery model and observation recovery model. Unlike traditional approaches reliant solely on reward signals, RPM incorporates temporal information. In addition, it allows the inclusion of extra knowledge or information from virtual training environments. This study designs UAV target search and UAV cooperative obstacle avoidance tasks. The algorithm outperforms baselines in these two environments.

It is important to note that UAVPM does not play a role in the inference phase. This means that the representation model and policy remain independent of UAVPM. Consequently, this study can introduce additional “cheating” information from virtual training environments to guide the UAV representation without concerns about its real-world existence. By leveraging historical information more effectively, this study enhances UAVs’ decision-making abilities, thus improving the performance of both tasks at hand.

The purpose of this paper is to design an output-feedback algorithm based on low-power observer (LPO), robust chattering-free controller and nonlinear disturbance observer (DO) to achieve trajectory tracking of quadrotor in the Cartesian plane.

To achieve trajectory tracking control, firstly the decoupled rotational and translational model of quadrotor are modified by introducing backstepped state-space variables. In the second step, robust integral sliding mode control is designed based on the proportional-integral-derivative (PID) technique. In the third step, a DO is constructed. In next step, the measurable outputs, i.e. rotational and translational state variables, are used to design the LPO. Finally, in the control algorithm all state variables and its rates are replaced with its estimates obtained using the state-observer.

The finding includes output-feedback control (OFC) algorithm designed by using a LPO. A modified backstepping model for rotational and rotational systems is developed prior to the design of integral sliding mode control based on PID technique. Unlike traditional high-gain observers (HGO), this paper used the LPO for state estimation of quadrotor systems to solve the problem of peaking phenomenon in HGO. Furthermore, a nonlinear DO is designed such that it attenuates disturbance with unknown magnitude and frequency. Moreover, a chattering reduction criterion has been introduced to solve the inherited chattering issue of controllers based on sliding mode technique.

This paper presents input and output data-driven model-free control algorithm. That is, only input and output of the quadrotor model are required to achieve the trajectory tracking control. Therefore, for practical implementation, the number of on-board sensor is reduced.

Although extensive research has been done for designing OFC algorithms for quadrotor, LPO has never been implemented for the rotational and translational state estimations of quadrotor. Furthermore, the mathematical model of rotational and translational systems is modified by using backstepped variables followed by the controller designed using PID and integral sliding mode control technique. Moreover, a DO is developed for attenuation of disturbance with unknown bound, magnitude and frequency.

This research aims to present a novel cooperative control architecture designed specifically for roads with variations in height and curvature. The primary objective is to enhance the longitudinal and lateral tracking accuracy of the vehicle.

In addressing the challenges posed by time-varying road information and vehicle dynamics parameters, a combination of model predictive control (MPC) and active disturbance rejection control (ADRC) is employed in this study. A coupled controller based on the authors’ model was developed by utilizing the capabilities of MPC and ADRC. Emphasis is placed on the ramifications of road undulations and changes in curvature concerning control effectiveness. Recognizing these factors as disturbances, measures are taken to offset their influences within the system. Load transfer due to variations in road parameters has been considered and integrated into the design of the authors’ synergistic architecture.

The framework's efficacy is validated through hardware-in-the-loop simulation. Experimental results show that the integrated controller is more robust than conventional MPC and PID controllers. Consequently, the integrated controller improves the vehicle's driving stability and safety.

The proposed coupled control strategy notably enhances vehicle stability and reduces slip concerns. A tailored model is introduced integrating a control strategy based on MPC and ADRC which takes into account vertical and longitudinal force variations and allowing it to effectively cope with complex scenarios and multifaceted constraints problems.

Conventional isolated dc–dc converters offer an efficient solution for performing voltage conversion with a large improved voltage gain. However, the small-signal analysis of these converters shows that a right-half-plane (RHP) zero appears in their control-to-output transfer function, exhibiting a nonminimum-phase stability. This RHP zero can limit the frequency response and dynamic specifications of the converters; therefore, the output voltage response is sluggish. To overcome these problems, the purpose of this study is to analyze, model and design a new isolated forward single-ended primary-inductor converter (IFSEPIC) through RHP zero alleviation.

At first, the normal operation of the suggested IFSEPIC is studied. Then, its average model and control-to-output transfer function are derived. Based on the obtained model and Routh–Hurwitz criterion, the components are suitably designed for the proposed IFSEPIC, such that the derived dynamic model can eliminate the RHP zero.

The advantages of the proposed IFSEPIC can be summarized as: This converter can provide conditions to achieve fast dynamic behavior and minimum-phase stability, owing to the RHP zero cancellation; with respect to conventional isolated converters, a larger gain can be realized using the proposed topology; thus, it is possible to attain a smaller operating duty cycle; for conventional isolated converters, transformer core saturation is a major concern, owing to a large magnetizing current. However, the average value of the magnetizing current becomes zero for the proposed IFSEPIC, thereby avoiding core saturation, particularly at high frequencies; and the input current of the proposed converter is continuous, reducing input current ripple.

The key benefits of the proposed IFSEPIC are shown via comparisons. To validate the design method and theoretical findings, a practical implementation is presented.

This study aims to realize efficient, fast and safe robot search task, the belief criteria decision-making approach is proposed to solve the object search task with an uncertain location.

The study formulates the robot search task as a partially observable Markov decision process, uses the semantic information to evaluate the belief state and designs the belief criteria decision-making approach. A cost function considering a trade-off among belief state, path length and movement effort is modelled to select the next best location in path planning.

The semantic information is successfully modelled and propagated, which can represent the belief of finding object. The belief criteria decision-making (BCDM) approach is evaluated in both Gazebo simulation platform and physical experiments. Compared to greedy, uniform and random methods, the performance index of path length and execution time is superior by BCDM approach.

The prior knowledge of robot working environment, especially semantic information, can be used for path planning to achieve efficient task execution in path length and execution time. The modelling and updating of environment information can lead a promising research topic to realize a more intelligent decision-making method for object search task.

This paper aims to Solar photovoltaic (PV) power can significantly impact the power system because of its intermittent nature. Hence, an accurate solar PV power forecasting model is required for appropriate power system planning.

In this paper, a long short-term memory (LSTM)-based double deep Q-learning (DDQL) neural network (NN) is proposed for forecasting solar PV power indirectly over the long-term horizon. The past solar irradiance, temperature and wind speed are used for forecasting the solar PV power for a place using the proposed forecasting model.

The LSTM-based DDQL NN reduces over- and underestimation and avoids gradient vanishing. Thus, the proposed model improves the forecasting accuracy of solar PV power using deep learning techniques (DLTs). In addition, the proposed model requires less training time and forecasts solar PV power with improved stability.

The proposed model is trained and validated for several places with different climatic patterns and seasons. The proposed model is also tested for a place with a temperate climatic pattern by constructing an experimental solar PV system. The training, validation and testing results have confirmed the practicality of the proposed solar PV power forecasting model using LSTM-based DDQL NN.

Throughout the 21st century, US households have experienced unprecedented levels of leverage. This dynamic has been exacerbated by income shortfalls during the COVID-19 crisis. Leveraging and deleveraging decisions affect household consumption. This study investigates the effect of the dynamics of household leverage and consumption on the stock market.

The authors explore the relation between household leverage and consumption in the context of the consumption capital asset pricing model (CCAPM). The authors test the model's implication that leverage has a negative risk premium by transforming the asset pricing restriction into an unconditional linear factor model and estimate the model using the general method of moments procedure. The authors run time-series regressions to estimate individual stocks' exposures to leverage, and cross-sectional regressions to investigate the leverage risk premium.

The authors show that shocks to household debt have strong and lasting effects on consumption growth. The authors extend the CCAPM to accommodate this effect and find, using various test assets, a negative risk premium associated with household deleveraging. Looking at individual stocks the authors show that the deleveraging risk premium is not explained by well-known risk factors.

This paper contributes to the literature on the role of leverage in economics and finance by establishing a relation between household leverage and spending decisions. The authors provide novel evidence that households' leveraging and deleveraging decisions can be a fundamental and influential force in determining asset prices. Further, this paper argues that household leverage might explain the small, persistent, and predictable component in consumption growth hypothesised in the long-run risk asset pricing literature.