Optimization over state feedback policies for robust control with constraints

This paper is concerned with the optimal control of linear discrete-time systems subject to unknown but bounded state disturbances and mixed polytopic constraints on the state and input. It is shown that the class of admissible affine state feedback control policies with knowledge of prior states is equivalent to the class of admissible feedback policies that are affine functions of the past disturbance sequence. This implies that a broad class of constrained finite horizon robust and optimal control problems, where the optimization is over affine state feedback policies, can be solved in a computationally efficient fashion using convex optimization methods. This equivalence result is used to design a robust receding horizon control (RHC) state feedback policy such that the closed-loop system is input-to-state stable (ISS) and the constraints are satisfied for all time and all allowable disturbance sequences. The cost to be minimized in the associated finite horizon optimal control problem is quadratic in the disturbance-free state and input sequences. The value of the receding horizon control law can be calculated at each sample instant using a single, tractable and convex quadratic program (QP) if the disturbance set is polytopic, or a tractable second-order cone program (SOCP) if the disturbance set is given by a 2-norm bound.     

Input-to-state stability of robust receding horizon control with an expected value cost

This paper is concerned with the stability of a class of receding horizon control (RHC) laws for constrained linear discrete-time systems subject to bounded state disturbances and convex state and input constraints. The paper considers the class of finite horizon feedback control policies parameterized as affine functions of the system state, calculation of which can be shown to be tractable via a convex reparameterization. When minimizing the expected value of a finite horizon quadratic cost, we show that the value function is convex. When solving this optimal control problem at each time step and implementing the result in a receding horizon fashion, we provide sufficient conditions under which the closed-loop system is input-to-state stable (ISS).     

Stochastic Receding Horizon Control of Constrained Linear Systems With State and Control Multiplicative Noise

We develop a receding horizon control approach to stochastic linear systems with control and state multiplicative noise that also contain constraints. Our receding horizon formulation is based upon an on-line optimization that utilizes open-loop plus linear feedback and is solved as a semi-definite programming problem. We also provide a characterization of stability, performance, and constraint satisfaction properties of the receding horizon controlled system under a specific choice of terminal weight and terminal constraint. A simple numerical example is used to illustrate the approach.      

Output feedback receding horizon control of constrained systems

This paper considers output feedback control of linear discrete-time systems with convex state and input constraints which are subject to bounded state disturbances and output measurement errors. We show that the non-convex problem of finding a constraint admissible affine output feedback policy over a finite horizon, to be used in conjunction with a fixed linear state observer, can be converted to an equivalent convex problem. When used in the design of a time-varying robust receding horizon control law, we derive conditions under which the resulting closed-loop system is guaranteed to satisfy the system constraints for all time, given an initial state estimate and bound on the state estimation error. When the state estimation error bound matches the minimal robust positively invariant (mRPI) set for the system error dynamics, we show that this control law is time-invariant, but its calculation generally requires solution of an infinite-dimensional optimization problem. Finally, using an invariant outer approximation to the mRPI error set, we develop a time-invariant control law that can be computed by solving a finite-dimensional tractable optimization problem at each time step that guarantees that the closed-loop system satisfies the constraints for all time.     

Input-to-state stability of hybrid systems with receding horizon control in the presence of packet dropouts

We analyze the stability of a constrained piecewise continuous hybrid system that is controlled by a receding horizon controller across an unreliable communication channel. We assume the presence of a buffer at the actuator to store the control input sequence received from the controller to compensate for any possible packet dropouts in future transmissions. Input-to-state stability is considered under the assumption that the number of consecutive packet dropouts is bounded using tightened state constraints in the optimization problem solved by the controller.     

On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach

In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, a particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state constraints. Due to the nature of the dynamical system and the constraints, we consider a one-step receding horizon. Using inverse cumulative distribution function, we convert the probabilistic state constraints to deterministic constraints, and obtain a tractable deterministic receding horizon control problem. We consider the receding horizon control law to have a linear state-feedback and an admissible offset term. We ensure mean square boundedness of the state variable via solving linear matrix inequalities off-line, and solve the receding horizon control problem on-line with control offset terms. We illustrate the overall approach applied on a macroeconomic system.     

用连续Hopfield网络实现无限时域上的最优控制

为避免直接采用Riccati方程求解时变系统无限域最优控制问题时的计算困难,本文提出一种基于时间连续状态连续型Hopfield网络(CTCSHNN)实现无限域动态最优控制的方法．该方法通过建立CTCSHNN能量函数与移动域控制指标间的等价关系,可在线构建CTCSHNN．理论分析表明,依据该方法设计的CTCSHNN具有稳定性,而且移动域控制量可由网络稳态输出直接产生．将该方法与滚动优化策略相结合,可实现无限时域上的闭环最优控制．仿真实验验证了理论设计的正确性与采用基于CTCSHNN的移动域控制实现无限域闭环最优控制的可行性．     

Stochastic tube MPC with state estimation

An output feedback Model Predictive Control (MPC) strategy for linear systems with additive stochastic disturbances and probabilistic constraints is proposed. Given the probability distributions of the disturbance input, the measurement noise and the initial state estimation error, the distributions of future realizations of the constrained variables are predicted using the dynamics of the plant and a linear state estimator. From these distributions, a set of deterministic constraints is computed for the predictions of a nominal model. The constraints are incorporated in a receding horizon optimization of an expected quadratic cost, which is formulated as a quadratic program. The constraints are constructed so as to provide a guarantee of recursive feasibility, and the closed loop system is stable in a mean-square sense. All uncertainties in this paper are taken to be bounded—in most control applications this gives a more realistic representation of process and measurement noise than the more traditional Gaussian assumption.     

Two-person zero-sum Markov games: receding horizon approach

We consider a receding horizon approach as an approximate solution to two-person zero-sum Markov games with infinite horizon discounted cost and average cost criteria. We first present error bounds from the optimal equilibrium value of the game when both players take "correlated" receding horizon policies that are based on exact or approximate solutions of receding finite horizon subgames. Motivated by the worst-case optimal control of queueing systems by Altman, we then analyze error bounds when the minimizer plays the (approximate) receding horizon control and the maximizer plays the worst case policy. We finally discuss some state-space size independent methods to compute the value of the subgame approximately for the approximate receding horizon control, along with heuristic receding horizon policies for the minimizer.     

On Stability of Constrained Receding Horizon Control with Finite Terminal Weighting Matrix

In this paper, a new stabilizing receding horizon control, based on a finite input and state horizon cost with a finite terminal weighting matrix, is proposed for time-varying discrete linear systems with constraints. We propose matrix inequality conditions on the terminal weighting matrix under which closed-loop stability is guaranteed for both cases of unconstrained and constrained systems with input and state constraints. We show that such a terminal weighting matrix can be obtained by solving a linear matrix inequality (LMI). In the case of constrained time-invariant systems, an artificial invariant ellipsoid constraint is introduced in order to relax the conventional terminal equality constraint and to handle constraints. Using the invariant ellipsoid constraints, a feasibility condition of the optimization problem is presented and a region of attraction is characterized for constrained systems with the proposed receding horizon control.     

Numerical optimization method for HJI equations derived from robust receding horizon control schemes and controller design

This paper addresses how to numerically solve the Hamilton-Jacobin-Isaac(HJI)equations derived from the robust receding horizon control schemes.The developed numerical method,the finite dierence scheme with sigmoidal transformation,is a stable and convergent algorithm for HJI equations.A boundary value iteration procedure is developed to increase the calculation accuracy with less time consumption.The obtained value function can be applied to the robust receding horizon controller design of some kind of uncertain nonlinear systems.In the controller design,the finite time horizon is extended into the infinite time horizon and the controller can be implemented in real time.It can avoid the on-line repeated optimization and the dependence on the feasibility of the initial state which are encountered in the traditional robust receding horizon control schemes.     

Q-PSO: Fast Quaternion-Based Pose Estimation from RGB-D Images

This paper investigates the leader–follower formation control problem for a group of networked nonholonomic mobile robots that are subject to bounded time-varying communication delays and an asynchronous clock. First we convert the formation control problem into a trajectory tracking problem, and then a fully distributed unified control framework based on the receding horizon control is implemented to converge the tracking errors. By adding an auxiliary acceleration term into the receding horizon controller, the framework is able to solve the impractical velocity jump problem. Considering the time-varying delays, the timing and order features of the messages are utilized to guarantee their logical correctness. To compensate for the delay effect, an improved control framework that exploits the predictability of the receding horizon controller is proposed. The asynchronous clock problem, which makes the communication delay unmeasurable, is studied. We give a definition of the syn point that is inspired from investigation of the property that messages are received out of order in a bounded time-varying delayed network. A novel method that detects the occurrence of syn points is integrated into the control framework to solve the asynchronous clock problem. Finally the effectiveness of the proposed approaches is demonstrated in the Player/Stage simulation environment.     

Piece-wise constant predictive feedback control of nonlinear systems

We investigate the problem of receding horizon control for a class of nonlinear processes. A computationally efficient method is developed to identify the optimal control action with respect to predefined performance criteria. Using Carleman linearization and assuming piece-wise constant control action, the state vector is discretized explicitly in time. The optimal control problem is then reformulated as a nonlinear optimization problem and is efficiently solved using analytically computed sensitivity functions and standard gradient-based algorithms.     

Design of receding horizon controls for constrained time-varying systems

In this note, we propose a generalized stabilizing receding horizon control scheme for input/state constrained linear discrete time-varying systems that improves feasibility and on-line computation on the constrained finite-horizon optimization problem, compared with existing schemes. The control scheme is based on a time-varying horizon cost function with time-varying terminal weighting matrices, which can easily be implemented via linear matrix inequality technique. We discuss modifications of the proposed scheme that improve feasibility or on-line computation time. Through simulation examples, we illustrate the results of these schemes.     

State-dependent Control of a Single Stage Hybrid System with Poisson Arrivals

We consider a single-stage hybrid manufacturing system where jobs arrive according to a Poisson process. These jobs undergo a deterministic process which is controllable. We define a stochastic hybrid optimal control problem and decompose it hierarchically to a lower-level and a higher-level problem. The lower-level problem is a deterministic optimal control problem solved by means of calculus of variations. We concentrate on the stochastic discrete-event control problem at the higher level, where the objective is to determine the service times of jobs. Employing a cost structure composed of process costs that are decreasing and strictly convex in service times, and system-time costs that are linear in system times, we show that receding horizon controllers are state-dependent controllers, where state is defined as the system size. In order to improve upon receding horizon controllers, we search for better state-dependent control policies and present two methods to obtain them. These stochastic-approximation-type methods utilize gradient estimators based on Infinitesimal Perturbation Analysis or Imbedded Markov Chain techniques. A numerical example demonstrates the performance improvements due to the proposed methods.     

Robust receding horizon control of constrained nonlinear systems

We present a method for the construction of a robust dual-mode, receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error. The controller is dual-mode. In a neighborhood of the origin, the control action is generated by a linear feedback controller designed for the linearized system. Outside this neighborhood, receding horizon control is employed. Existing receding horizon controllers for nonlinear, continuous time systems, which are guaranteed to stabilize the nonlinear system to which they are applied, require the exact solution, at every instant, of an optimal control problem with terminal equality constraints. These requirements are considerably relaxed in the dual-mode receding horizon controller presented in this paper. Stability is achieved by imposing a terminal inequality, rather than an equality, constraint. Only approximate minimization is required. A variable time horizon is permitted. Robustness is achieved by employing conservative state and stability constraint sets, thereby permitting a margin of error. The resultant dual-mode controller requires considerably less online computation than existing receding horizon controllers for nonlinear, constrained systems     

Disturbance attenuation for constrained discrete-time systems via receding horizon controls

In this note, we propose new receding horizon H/sub /spl infin// control (RHHC) schemes for linear input-constrained discrete time-invariant systems with disturbances. The proposed control schemes are based on the dynamic game problem of a finite-horizon cost function with a fixed finite terminal weighting matrix and a one-horizon cost function with time-varying finite terminal weighting matrices, respectively. We show that the resulting RHHCs guarantee closed-loop stability in the absence of disturbances and H/sub /spl infin// norm bound for 2-norm bounded disturbances. We also show that the proposed schemes can easily be implemented via linear matrix inequality optimization. We illustrate the effectiveness of the proposed schemes through simulations.     

带有内动态的离散不确定非线性系统的滑模预测跟踪控制

对于一类带有内动态的单输入-单输出不确定离散非线性系统,基于滑模预测控制技术设计了一个控制器.通过反馈校正和滚动优化技术,可以及时补偿不确定性的影响,提高了匹配和不匹配不确定项的鲁棒性.然后,通过滚动优化技术得到期望的滑模控制律.特别地,通过预测控制,滑模控制的抖振现象可以消除.最后,在不确定项的界未知的情况下,得到闭环系统的所有信号都是有界的,并且跟踪误差是鲁棒稳定的.仿真例子说明所提出控制方法的有效性.     

Constrained RHC for LPV systems with bounded rates of parameter variations

This paper studies a stabilization problem of polytopically uncertain linear parameter varying systems with input constraints and bounded rates of parameter variations. In the framework of finite receding horizon control (RHC), a system containing “parameter” uncertainties is modified into a system with “parameter-incremental” uncertainties within each horizon. For the system modified in this manner, a robust RHC is designed by solving an optimization problem at each time instant. Based on the feasibility of the problem and the optimality of its solution, the closed-loop system stability is guaranteed. A numerical example is included to illustrate the validity of the results.     

基于终端不变集的 Markov 跳变系统约束预测控制

针对离散 Markov 跳变系统, 研究带输入输出约束的有限时域预测控制问题. 对于给定预测时域内的每条模态轨迹, 设计控制输入序列, 驱动系统状态到达相应的终端不变集内, 在预测时域外, 则寻求一个虚拟的状态反馈控制器以保证系统的随机稳定性, 在此基础上, 分别给出了以线性矩阵不等式 (LMI) 描述的带输入、输出约束预测控制器的设计方法.