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Article
Publication date: 1 December 1997

I.N. Egorov, G.V. Kretinin and I.A. Leshchenko

Discusses a new approach to solving optimal designing and control problems in aircraft gas‐turbine engine components. This approach is a combination of optimal designing problems…

1084

Abstract

Discusses a new approach to solving optimal designing and control problems in aircraft gas‐turbine engine components. This approach is a combination of optimal designing problems with optimal control problems, allowing the formation of a single problem of optimal designing of controllable systems. The solving of this problem would involve simultaneous optimization of both design parameters and control laws. Allows the making of technically correct and substantiated decisions, taking into consideration several efficiency criteria for gas‐turbine engine components; a specific feature being the determination of a set of competitive optimal solutions in terms of different efficiency criteria values. Demonstrates the effectiveness of this approach by an example of multicriteria design optimization of a controllable axial flow compressor. Presents the results of a search of compressor blade rows geometrical parameters sets and of compressor stator blades control laws which are Edgeworth‐Pareto optimal for four operating modes. Shows a possibility of increasing compressor efficiency considerably by choosing the most preferable design parameters set and implementing in airborne digital control system a number of control laws optimal for different operating modes.

Details

Aircraft Engineering and Aerospace Technology, vol. 69 no. 6
Type: Research Article
ISSN: 0002-2667

Keywords

Article
Publication date: 1 September 2004

Hao Hua Ning

This paper presents an optimal design method of number and placements of piezoelectric patch actuators in active vibration control of a plate. Eigenvalue distribution of energy…

Abstract

This paper presents an optimal design method of number and placements of piezoelectric patch actuators in active vibration control of a plate. Eigenvalue distribution of energy correlative matrix of control input force is applied to determine optimal number of the required actuators. Genetic algorithms (GAs) using active vibration control effects, which are taken as the objective function, are adopted to search optimal placements of actuators. The results show that disturbance exerted on a plate is a key factor of determining optimal number and placements of actuators in active structural vibration control, and a global and efficient optimization solution of multiple actuator placements can be obtained using GAs.

Details

Engineering Computations, vol. 21 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 28 February 2020

Alexander Zemliak and Jorge Espinosa-Garcia

In this paper, on the basis of a previously developed approach to circuit optimization, the main element of which is the control vector that changes the form of the basic…

Abstract

Purpose

In this paper, on the basis of a previously developed approach to circuit optimization, the main element of which is the control vector that changes the form of the basic equations, the structure of the control vector is determined, which minimizes CPU time.

Design/methodology/approach

The circuit optimization process is defined as a controlled dynamic system with a special control vector. This vector serves as the main tool for generalizing the problem of circuit optimization and produces a huge number of different optimization strategies. The task of finding the best optimization strategy that minimizes processor time can be formulated. There is a need to find the optimal structure of the control vector that minimizes processor time. A special function, which is a combination of the Lyapunov function of the optimization process and its time derivative, was proposed to predict the optimal structure of the control vector. The found optimal positions of the switching points of the control vector give a large gain in CPU time in comparison with the traditional approach.

Findings

The optimal positions of the switching points of the components of the control vector were calculated. They minimize processor time. Numerical results are obtained for various circuits.

Originality/value

The Lyapunov function, which is one of the main characteristics of any dynamic system, is used to determine the optimal structure of the control vector, which minimizes the time of the circuit optimization process.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 39 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 January 2014

Mohammad Mehdi Fateh and Maryam Baluchzadeh

Applying discrete linear optimal control to robot manipulators faces two challenging problems, namely nonlinearity and uncertainty. This paper aims to overcome nonlinearity and…

Abstract

Purpose

Applying discrete linear optimal control to robot manipulators faces two challenging problems, namely nonlinearity and uncertainty. This paper aims to overcome nonlinearity and uncertainty to design the discrete optimal control for electrically driven robot manipulators.

Design/methodology/approach

Two novel discrete optimal control approaches are presented. In the first approach, a control-oriented model is applied for the discrete linear quadratic control while modeling error is estimated and compensated by a robust time-delay controller. Instead of the torque control strategy, the voltage control strategy is used for obtaining an optimal control that is free from the manipulator dynamics. In the second approach, a discrete optimal controller is designed by using a particle swarm optimization algorithm.

Findings

The first controller can overcome uncertainties, guarantee stability and provide a good tracking performance by using an online optimal algorithm whereas the second controller is an off-line optimal algorithm. The first control approach is verified by stability analysis. A comparison through simulations on a three-link electrically driven robot manipulator shows superiority of the first approach over the second approach. Another comparison shows that the first approach is superior to a bounded torque control approach in the presence of uncertainties.

Originality/value

The originality of this paper is to present two novel optimal control approaches for tracking control of electrically driven robot manipulators with considering the actuator dynamics. The novelty is that the proposed control approaches are free from the robot's model by using the voltage control strategy. The first approach is a novel discrete linear quadratic control design supported by a time-delay uncertainty compensator. The second approach is an off-line optimal design by using the particle swarm optimization.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 33 no. 1/2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 15 March 2013

Xiaoning Shi, Jifeng Guo, Naigang Cui and Rong Huang

The purpose of this paper is to design a solar sail heliocentric transfer orbit which can meet the requirements of control system and capture orbit, and to provide the change of…

Abstract

Purpose

The purpose of this paper is to design a solar sail heliocentric transfer orbit which can meet the requirements of control system and capture orbit, and to provide the change of angles for attitude control system.

Design/methodology/approach

Aiming at the problem of solar sail heliocentric transfer orbits design, this paper addresses the derivation of analytical optimal control law. The control laws can realize the combination of the control of each orbit element, but they can only give local optimal solution to meet the practical needs of mission. In order to solve this problem and meet the capture orbit and the attitude control system requirements, the modified genetic algorithm based on the analytical control law is introduced.

Findings

The algorithm addressed by this paper includes results closer to the global optimization, and also can meet the engineering constraints.

Practical implications

The analytical optimal control law can be applied to the future onboard sail control systems. The blending optimal algorithm is demonstrated to be suitable as a method of preliminary design for solar sail deep space exploration mission.

Originality/value

A blending optimal algorithm combining the analytical control law and genetic algorithm is proposed; the algorithm can search for global optimization based on the local optimal results of analytical control law.

Details

Aircraft Engineering and Aerospace Technology, vol. 85 no. 2
Type: Research Article
ISSN: 0002-2667

Keywords

Abstract

Details

Optimal Growth Economics: An Investigation of the Contemporary Issues and the Prospect for Sustainable Growth
Type: Book
ISBN: 978-0-44450-860-7

Article
Publication date: 12 September 2023

Gerasimos G. Rigatos, Masoud Abbaszadeh, Pierluigi Siano and Jorge Pomares

Permanent magnet synchronous spherical motors can have wide use in robotics and industrial automation. They enable three-DOF omnidirectional motion of their rotor. They are…

Abstract

Purpose

Permanent magnet synchronous spherical motors can have wide use in robotics and industrial automation. They enable three-DOF omnidirectional motion of their rotor. They are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. Unlike conventional synchronous motors, permanent magnet synchronous spherical motors consist of a fixed inner shell, which is the stator, and a rotating outer shell, which is the rotor. Their dynamic model is multivariable and strongly nonlinear. The treatment of the associated control problem is important.

Design/methodology/approach

In this paper, the multivariable dynamic model of permanent magnet synchronous spherical motors is analysed, and a nonlinear optimal (H-infinity) control method is developed for it. Differential flatness properties are proven for the spherical motors’ state-space model. Next, the motors’ state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a time-varying operating point, which is defined by the present value of the motors’ state vector and by the last sampled value of the control input vector. For the approximately linearized model of the permanent magnet synchronous spherical motors, a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains, an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach implemented in successive loops.

Findings

Due to the nonlinear and multivariable structure of the state-space model of spherical motors, the solution of the associated nonlinear control problem is a nontrivial task. In this paper, a novel nonlinear optimal (H-infinity) control approach is proposed for the dynamic model of permanent magnet synchronous spherical motors. The method is based on approximate linearization of the motor’s state-space model with the use of first-order Taylor series expansion and the computation of the associated Jacobian matrices. Furthermore, the paper has introduced a different solution to the nonlinear control problem of the permanent magnet synchronous spherical motor, which is based on flatness-based control implemented in successive loops.

Research limitations/implications

The presented control approaches do not exhibit any limitations, but on the contrary, they have specific advantages. In comparison to global linearization-based control schemes (such as Lie-algebra-based control), they do not make use of complicated changes of state variables (diffeomorphisms) and transformations of the system's state-space description. The computed control inputs are applied directly to the initial nonlinear state-space model of the permanent magnet spherical motor without the intervention of inverse transformations and thus without coming against the risk of singularities.

Practical implications

The motion control problem of spherical motors is nontrivial because of the complicated nonlinear and multivariable dynamics of these electric machines. So far, there have been several attempts to apply nonlinear feedback control to permanent magnet-synchronous spherical motors. However, due to the model’s complexity, few results exist about the associated nonlinear optimal control problem. The proposed nonlinear control methods for permanent magnet synchronous spherical motors make more efficient, precise and reliable the use of such motors in robotics, electric traction and several automation systems.

Social implications

The treated research topic is central for robotic and industrial automation. Permanent magnet synchronous spherical motors are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. The solution of the control problem for the nonlinear dynamic model of permanent magnet synchronous spherical motors has many industrial applications and therefore contributes to economic growth and development.

Originality/value

The proposed nonlinear optimal control method is novel compared to past attempts to solve the optimal control problem for nonlinear dynamical systems. Unlike past approaches, in the new nonlinear optimal control method, linearization is performed 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 and not at points that belong to the desirable trajectory (setpoints). Besides, the Riccati equation which is used for computing the feedback gains of the controller is new, and so is the global stability proof for this control method. Compared to nonlinear model predictive control, which is a popular approach for treating the optimal control problem in industry, the new nonlinear optimal (H-infinity) control scheme is of proven global stability, and the convergence of its iterative search for the optimum does not depend on initial conditions and trials with multiple sets of controller parameters. It is also noteworthy that 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 into the linear parameter varying 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. Furthermore, the second control method proposed in this paper, which is flatness-based control in successive loops, is also novel and demonstrates substantial contribution to nonlinear control for robotics and industrial automation.

Article
Publication date: 25 July 2023

Gerasimos G. Rigatos, Masoud Abbaszadeh, Bilal Sari and Jorge Pomares

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…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Research limitations/implications

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.

Practical implications

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.

Social implications

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.

Originality/value

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.

Details

International Journal of Intelligent Unmanned Systems, vol. 12 no. 1
Type: Research Article
ISSN: 2049-6427

Keywords

Article
Publication date: 6 June 2023

Gerasimos G. Rigatos, Masoud Abbaszadeh, Fabrizio Marignetti and Pierluigi Siano

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as…

Abstract

Purpose

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as in the traction of transportation systems (such as electric vehicles and electric trains or ships with electric propulsion). The dynamic model of VSI-PMSMs is multivariable and exhibits complicated nonlinear dynamics. The inverters’ currents, which are generated through a pulsewidth modulation process, are used to control the stator currents of the PMSM, which in turn control the rotational speed of this electric machine. So far, several nonlinear control schemes for VSI-PMSMs have been developed, having as primary objectives the precise tracking of setpoints by the system’s state variables and robustness to parametric changes or external perturbations. However, little has been done for the solution of the associated nonlinear optimal control problem. The purpose of this study/paper is to provide a novel nonlinear optimal control method for VSI-fed three-phase PMSMs.

Design/methodology/approach

The present article proposes a nonlinear optimal control approach for VSI-PMSMs. The nonlinear dynamic model of VSI-PMSMs undergoes approximate linearization around a temporary operating point, which is recomputed at each iteration of the control method. This temporary operating point is defined by the present value of the voltage source inverter-fed PMSM state vector and by the last sampled value of the motor’s control input vector. The linearization relies on Taylor series expansion and the calculation of the system’s Jacobian matrices. For the approximately linearized model of the voltage source inverter-fed PMSM, an H-infinity feedback controller is designed. For the computation of the controller’s feedback gains, an algebraic Riccati equation is iteratively solved at each time-step of the control method. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control for this system, the H-infinity Kalman filter is proposed as a state observer. The proposed control method achieves fast and accurate tracking of the reference setpoints of the VSI-fed PMSM under moderate variations of the control inputs.

Findings

The proposed H-infinity controller provides the solution to the optimal control problem for the VSI-PMSM system under model uncertainty and external perturbations. Actually, this controller represents a min–max differential game taking place between the control inputs, which try to minimize a cost function that contains a quadratic term of the state vector’s tracking error, the model uncertainty, and exogenous disturbance terms, which try to maximize this cost function. To select the feedback gains of the stabilizing feedback controller, an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. To analyze the stability properties of the control scheme, the Lyapunov method is used. It is proven that the VSI-PMSM loop has the H-infinity tracking performance property, which signifies robustness against model uncertainty and disturbances. Moreover, under moderate conditions, the global asymptotic stability properties of this control scheme are proven. The proposed control method achieves fast tracking of reference setpoints by the VSI-PMSM state variables, while keeping also moderate the variations of the control inputs. The latter property indicates that energy consumption by the VSI-PMSM control loop can be minimized.

Practical implications

The proposed nonlinear optimal control method for the VSI-PMSM system exhibits several advantages: Comparing to global linearization-based control methods, such as Lie algebra-based control or differential flatness theory-based control, the nonlinear optimal control scheme avoids complicated state variable transformations (diffeomorphisms). Besides, its control inputs are applied directly to the initial nonlinear model of the VSI-PMSM system, and thus inverse transformations and the related singularity problems are also avoided. Compared with backstepping control, the nonlinear optimal control scheme does not require the state-space description of the controlled system to be found in the triangular (backstepping integral) form. Compared with sliding-mode control, there is no need to define in an often intuitive manner the sliding surfaces of the controlled system. Finally, compared with local model-based control, the article’s nonlinear optimal control method avoids linearization around multiple operating points and does not need the solution of multiple Riccati equations or LMIs. As a result of this, the nonlinear optimal control method requires less computational effort.

Social implications

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as in the traction of transportation systems (such as electric vehicles and electric trains or ships with electric propulsion), The solution of the associated nonlinear control problem enables reliable and precise functioning of VSI-fd PMSMs. This in turn has a positive impact in all related industrial applications and in tasks of electric traction and propulsion where VSI-fed PMSMs are used. It is particularly important for electric transportation systems and for the wide use of electric vehicles as expected by green policies which aim at deploying electromotion and at achieving the Net Zero objective.

Originality/value

Unlike past approaches, in the new nonlinear optimal control method, linearization is performed 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 input vector and not at points that belong to the desirable trajectory (setpoints). Besides, the Riccati equation, which is used for computing the feedback gains of the controller, is new, as is the global stability proof for this control method. Comparing with nonlinear model predictive control, which is a popular approach for treating the optimal control problem in industry, the new nonlinear optimal (H-infinity) control scheme is of proven global stability, and the convergence of its iterative search for the optimum does not depend on initial conditions and trials with multiple sets of controller parameters. It is also noteworthy that 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 that can be transformed to the linear parameter varying 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.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 42 no. 6
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 8 January 2019

Tao Han, Bo Xiao, Xi-Sheng Zhan, Jie Wu and Hongling Gao

The purpose of this paper is to investigate time-optimal control problems for multiple unmanned aerial vehicle (UAV) systems to achieve predefined flying shape.

Abstract

Purpose

The purpose of this paper is to investigate time-optimal control problems for multiple unmanned aerial vehicle (UAV) systems to achieve predefined flying shape.

Design/methodology/approach

Two time-optimal protocols are proposed for the situations with or without human control input, respectively. Then, Pontryagin’s minimum principle approach is applied to deal with the time-optimal control problems for UAV systems, where the cost function, the initial and terminal conditions are given in advance. Moreover, necessary conditions are derived to ensure that the given performance index is optimal.

Findings

The effectiveness of the obtained time-optimal control protocols is verified by two contrastive numerical simulation examples. Consequently, the proposed protocols can successfully achieve the prescribed flying shape.

Originality/value

This paper proposes a solution to solve the time-optimal control problems for multiple UAV systems to achieve predefined flying shape.

Details

International Journal of Intelligent Computing and Cybernetics, vol. 12 no. 1
Type: Research Article
ISSN: 1756-378X

Keywords

1 – 10 of over 52000