A hybrid receding-horizon control scheme for nonlinear systems

A hybrid receding-horizon control scheme for nonlinear discrete-time systems is proposed. Whereas a set of optimal feedback control functions is defined at the continuous level, a discrete-event controller chooses the best control action, depending on the current conditions of a plant and on possible external events. Such a two-level scheme is embedded in the structure of abstract hybrid systems, thus making it possible to prove a new asymptotic stability result for the hybrid receding-horizon control approach.     

无穷时域的连续时间广义预测控制

将无穷时域的性能指标引入连续时间的广义预测控制,通过施加新的终端等式约束,把包含无穷时域性能指标的优化问题转化成可解的二次规划问题.利用后退时域性能指标的单调性,给出了保证连续时间广义预测控制闭环稳定性的条件.仿真例子验证了该算法的有效性.     

Uniting local and global controllers for uncertain nonlinear systems: beyond global inverse optimality

This paper provides a solution to a new problem of global robust control for uncertain nonlinear systems. A new recursive design of stabilizing feedback control is proposed in which inverse optimality is achieved globally through the selection of generalized state-dependent scaling. The inverse optimal control law can always be designed such that its linearization is identical to linear optimal control, i.e. optimal control, for the linearized system with respect to a prescribed quadratic cost functional. Like other backstepping methods, this design is always successful for systems in strict-feedback form. The significance of the result stems from the fact that our controllers achieve desired level of ‘global’ robustness which is prescribed a priori. By uniting locally optimal robust control and global robust control with global inverse optimality, one can obtain global control laws with reasonable robustness without solving Hamilton–Jacobi equations directly.     

基于递归神经网络的移动域控制方法

构造一种线性差分式Hopfield网络（LDHNN）,其稳定状态可使能量函数达到唯一极小值,利用该网络稳定性与其能量函数收敛特性的关系,提出了基于LDHNN的移动域控制方法,LDHNN的理论设计表明,网络的稳态输出即为移动域LQ控制问题的解,当系统满足一定条件时,基于LDHNN的移动域LQ控制能保证闭环最优控制系统的渐近稳定性．数字仿真取得了与理论分析一致的实验结果。     

Multi-agent consensus algorithm with obstacle avoidance via optimal control approach

Multi-agent consensus problem in an obstacle-laden environment is addressed in this study. A novel optimal control approach is proposed for the multi-agent system to reach consensus as well as avoid obstacles with a reasonable control effort. An innovative nonquadratic penalty function is constructed to achieve obstacle avoidance capability from an inverse optimal control perspective. The asymptotic stability and optimality of the consensus algorithm are proven. In addition, the optimal control law only requires local information from the communication topology to guarantee the proposed behaviour, rather than all agents’ information. The consensus and obstacle avoidance are validated through various simulations.     

Partial‐state stabilization and optimal feedback control

In this paper, we develop a unified framework to address the problem of optimal nonlinear analysis and feedback control for partial stability and partial‐state stabilization. Partial asymptotic stability of the closed‐loop nonlinear system is guaranteed by means of a Lyapunov function that is positive definite and decrescent with respect to part of the system state, which can clearly be seen to be the solution to the steady‐state form of the Hamilton–Jacobi–Bellman equation and hence guaranteeing both partial stability and optimality. The overall framework provides the foundation for extending optimal linear‐quadratic controller synthesis to nonlinear nonquadratic optimal partial‐state stabilization. Connections to optimal linear and nonlinear regulation for linear and nonlinear time‐varying systems with quadratic and nonlinear nonquadratic cost functionals are also provided. Finally, we also develop optimal feedback controllers for affine nonlinear systems using an inverse optimality framework tailored to the partial‐state stabilization problem and use this result to address polynomial and multilinear forms in the performance criterion. Copyright © 2015 John Wiley & Sons, Ltd.     

Inverse optimality in the class of Hopfield neural networks with input nonlinearity

This paper presents the chaos suppression problem in the class of Hopfield neural networks (HNNs) with input nonlinearity using inverse optimality approach. Using the inverse optimality technique and based on Lyapunov stability theory, a stabilizing control law, which is optimal with respect to meaningful cost functional, is determined to achieve global asymptotically stability in the closed-loop system. Numerical simulation is performed on a four-dimensional hyper-chaotic HNN to demonstrate the effectiveness of the proposed method.     

一类非线性耗散系统的逆最优控制

首先研究一类单输入非仿射非线性系统的逆最优控制问题, 其代价泛函为非线性-非二次型, 设计出一族参数化的状态反馈逆最优控制器;然后讨论当该系统为耗散系统时, 在供给率为二次型的耗散性理论框架下,给出使系统渐近稳定的李雅普诺夫函数和镇定控制律, 并通过适当选取代价泛函中的参数,使得李雅普诺夫函数也是最优值函数,进而揭示出耗散系统在线性输出反馈意义下稳定性与最优性之间的等价关系.     

Optimal consensus algorithm integrated with obstacle avoidance

This article proposes a new consensus algorithm for the networked single-integrator systems in an obstacle-laden environment. A novel optimal control approach is utilised to achieve not only multi-agent consensus but also obstacle avoidance capability with minimised control efforts. Three cost functional components are defined to fulfil the respective tasks. In particular, an innovative nonquadratic obstacle avoidance cost function is constructed from an inverse optimal control perspective. The other two components are designed to ensure consensus and constrain the control effort. The asymptotic stability and optimality are proven. In addition, the distributed and analytical optimal control law only requires local information based on the communication topology to guarantee the proposed behaviours, rather than all agents’ information. The consensus and obstacle avoidance are validated through simulations.     

An optimal regulation strategy with disturbance rejection for energy management of hybrid electric vehicles

The energy management problem of finding the optimal split between the different sources of energy in a charge-sustaining parallel HEV, ensuring stability and optimality with respect to a performance objective (fuel consumption minimization over a driving cycle), is addressed in this paper. The paper develops a generic stability and optimality framework within which the energy management problem is cast in the form of a nonlinear optimal regulation (with disturbance rejection) problem and a control Lyapunov function is used to design the control law. Two theorems ensuring optimality and asymptotic stability of the energy management strategy are proposed and proved. The sufficient conditions for optimality and stability are used to derive an analytical expression for the control law as a function of the battery state of charge/state of energy and system parameters. The control law is implemented in a simplified backward vehicle simulator and its performance is evaluated against the global optimal solution obtained from dynamic programming. The strategy performs within 4% of the benchmark solution while guaranteeing optimality and stability for any driving cycle.     

Locally optimal and robust backstepping design

For a class of nonlinear systems, a robust backstepping design achieves both local optimality and global inverse optimality. The design is robust in the sense that it achieves a prescribed level of disturbance attenuation with stability margins. An analytic example illustrates the performance of the locally optimal control design     

New path-generation based receding-horizon formulation for constrained stabilization of nonlinear systems

In this paper, a new formulation of constrained stabilizing receding-horizon control is proposed. This formulation is based on the use of open-loop steering path generators. The open-loop optimization problem associated to the proposed receding-horizon formulation is scalar in which the optimization variable is the prediction horizon length. Stability is proved in a sampling control scheme. A simple example is given to illustrate the main concepts.     

Cooperative Constrained Control of Distributed Agents With Nonlinear Dynamics and Delayed Information Exchange: A Stabilizing Receding-Horizon Approach

This paper addresses the problem of cooperative control of a team of distributed agents with decoupled nonlinear discrete-time dynamics, which operate in a common environment and exchange-delayed information between them. Each agent is assumed to evolve in discrete-time, based on locally computed control laws, which are computed by exchanging delayed state information with a subset of neighboring agents. The cooperative control problem is formulated in a receding-horizon framework, where the control laws depend on the local state variables (feedback action) and on delayed information gathered from cooperating neighboring agents (feedforward action). A rigorous stability analysis exploiting the input-to-state stability properties of the receding-horizon local control laws is carried out. The stability of the team of agents is then proved by utilizing small-gain theorem results.      

Nonlinear–nonquadratic optimal and inverse optimal control for stochastic dynamical systems

In this paper, we develop a unified framework to address the problem of optimal nonlinear analysis and feedback control for nonlinear stochastic dynamical systems. Specifically, we provide a simplified and tutorial framework for stochastic optimal control and focus on connections between stochastic Lyapunov theory and stochastic Hamilton–Jacobi–Bellman theory. In particular, we show that asymptotic stability in probability of the closed‐loop nonlinear system is guaranteed by means of a Lyapunov function that can clearly be seen to be the solution to the steady‐state form of the stochastic Hamilton–Jacobi–Bellman equation and, hence, guaranteeing both stochastic stability and optimality. In addition, we develop optimal feedback controllers for affine nonlinear systems using an inverse optimality framework tailored to the stochastic stabilization problem. These results are then used to provide extensions of the nonlinear feedback controllers obtained in the literature that minimize general polynomial and multilinear performance criteria. Copyright © 2017 John Wiley & Sons, Ltd.     

Inverse optimal stabilization of a rigid spacecraft

The authors present an approach for constructing optimal feedback control laws for regulation of a rotating rigid spacecraft. They employ the inverse optimal control approach which circumvents the task of solving a Hamilton-Jacobi equation and results in a controller optimal with respect to a meaningful cost functional. The inverse optimality approach requires the knowledge of a control Lyapunov function and a stabilizing control law of a particular form. For the spacecraft problem, they are both constructed using the method of integrator backstepping. The authors give a characterization of (nonlinear) stability margins achieved with the inverse optimal control law     

Stochastic differential games and inverse optimal control and stopper policies

In this paper, we consider a two-player stochastic differential game problem over an infinite time horizon where the players invoke controller and stopper strategies on a nonlinear stochastic differential game problem driven by Brownian motion. The optimal strategies for the two players are given explicitly by exploiting connections between stochastic Lyapunov stability theory and stochastic Hamilton–Jacobi–Isaacs theory. In particular, we show that asymptotic stability in probability of the differential game problem is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution to the steady-state form of the stochastic Hamilton–Jacobi–Isaacs equation, and hence, guaranteeing both stochastic stability and optimality of the closed-loop control and stopper policies. In addition, we develop optimal feedback controller and stopper policies for affine nonlinear systems using an inverse optimality framework tailored to the stochastic differential game problem. These results are then used to provide extensions of the linear feedback controller and stopper policies obtained in the literature to nonlinear feedback controllers and stoppers that minimise and maximise general polynomial and multilinear performance criteria.     

Closed-form control laws for linear time-varying systems

Closed-form control laws are developed for continuous, linear, time-varying (LTV) systems based on approximate solutions to a receding-horizon control problem. These control laws can be derived in the first- or higher order closed forms. Once obtained, the control laws need no explicit gain-scheduling or online integrations to implement. The notion of practical stability is used, and practical or uniform asymptotic stability of the closed-loop system, depending on conditions imposed on the system, is established     

A note on the receding-horizon control method

In this correspondence, the relation of receding-horizon control method with the state deadbeat control is brought out. It is shown for single-input systems that the receding-horizon control is a state deadbeat control if the horizon length is taken to be equal to the state dimension.     

On the robustness of receding-horizon control with terminalconstraints

Robustness properties of nonlinear receding-horizon controllers with zero terminal state constraints are investigated with respect to gain and additive perturbations. Some robustness margins are derived by extending to the receding-horizon case the analysis originally proposed by Geromel and da Cruz for infinite-horizon controllers. In the linear case, it is shown that the zero terminal state receding-horizon controller exhibits worse robustness margins compared to standard infinite-horizon LQ control     

基于遗传算法的锅炉水温PID控制寻优

遗传算法相比传统调节方法具有更好的鲁棒性和最优性。结合锅炉动态水温单回路控制系统的PID参数整定与优化问题,采用遗传算法对其参数进行优化。仿真结果表明,这种优化算法加快了收敛速度,有效提高了系统的全局稳定性,增强了PID控制器的鲁棒性。