本文提出了一种针对离散时间线性系统中任意时间不变概率不确定性和加性高斯过程噪声的随机模型预测控制方法。通过适当选择成本函数证明闭环稳定性，并利用多项式混沌进行系统动力学中的不确定性传播。通过Van de Vusse反应验证了该方法的性能。
英文摘要：
A stochastic model predictive control (SMPC) approach is presented for discrete-time linear systems with arbitrary time-invariant probabilistic uncertainties and additive Gaussian process noise. Closed-loop stability of the SMPC approach is established by appropriate selection of the cost function. Polynomial chaos is used for uncertainty propagation through system dynamics. The performance of the SMPC approach is demonstrated using the Van de Vusse reactions.
A receding horizon learning scheme is proposed to transfer the state of a discrete-time dynamical control system to zero without the need of a system model. Global state convergence to zero is proved for the class of stabilizable and detectable linear time-invariant systems, assuming that only input and output data is available and an upper bound of the state dimension is known. The proposed scheme consists of a receding horizon control scheme and a proximity-based estimation scheme to estimate and control the closed-loop trajectory. Simulations are presented for linear and nonlinear systems.
In this paper, we consider a Markov decision process (MDP), where the ego agent has a nominal objective to pursue while needs to hide its state from detection by an adversary. After formulating the problem, we first propose a value iteration (VI) approach to solve it. To overcome the "curse of dimensionality" and thus gain scalability to larger-sized problems, we then propose a receding-horizon optimization (RHO) approach to obtain approximate solutions. We use examples to illustrate and compare the VI and RHO approaches, and to show the potential of our problem formulation for practical appli…
We address the problem of simultaneously learning and control in an online receding horizon control setting. We consider the control of an unknown linear dynamical system with general cost functions and affine constraints on the control input. Our goal is to develop an online learning algorithm that minimizes the dynamic regret, which is defined as the difference between the cumulative cost incurred by the algorithm and that of the best policy with full knowledge of the system, cost functions and state and that satisfies the control input constraints. We propose a novel approach to explore in …
We address the multi-agent persistent monitoring problem defined on a set of nodes (targets) interconnected over a network topology. A measure of mean overall node state uncertainty evaluated over a finite period is to be minimized by controlling the motion of a cooperating team of agents. To address this problem, we propose an event-driven receding horizon control approach that is computationally efficient, distributed and on-line. The proposed controller differs from the existing on-line gradient-based parametric controllers and off-line greedy cycle search methods that often lead to either …
This paper addresses the persistent monitoring problem defined on a network where a set of nodes (targets) needs to be monitored by a team of dynamic energy-aware agents. The objective is to control the agents' motion to jointly optimize the overall agent energy consumption and a measure of overall node state uncertainty, evaluated over a finite period of interest. To achieve these objectives, we extend an established event-driven Receding Horizon Control (RHC) solution by adding an optimal controller to account for agent motion dynamics and associated energy consumption. The resulting RHC sol…
We propose a distributed data-based predictive control scheme to stabilize a network system described by linear dynamics. Agents cooperate to predict the future system evolution without knowledge of the dynamics, relying instead on learning a data-based representation from a single sample trajectory. We employ this representation to reformulate the finite-horizon Linear Quadratic Regulator problem as a network optimization with separable objective functions and locally expressible constraints. We show that the controller resulting from approximately solving this problem using a distributed opt…
On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach
CRAN–CNRS UMR 7039, Université de Lorraine（洛林大学）；Instituto Tecnologico de Hermosillo（埃莫西约理工学院）；Instistute of Mathematics “Simon Stoilow”, Romanian Academy（罗马尼亚科学院西蒙·斯托伊洛数学研究所）
A novel modelling framework is proposed for the analysis of aggregative games on an infinite-time horizon, assuming that players are subject to heterogeneous periodic constraints. A new aggregative equilibrium notion is presented and the strategic behaviour of the agents is analysed under a receding horizon paradigm. The evolution of the strategies predicted and implemented by the players over time is modelled through a discrete-time multi-valued dynamical system. By considering Lyapunov stability notions and applying limit and invariance results for set-valued correspondences, necessary condi…
Distributed energy storage and flexible loads are essential tools for ensuring stable and robust operation of the power grid in spite of the challenges arising from the integration of volatile renewable energy generation and increasing peak loads due to widespread electrification. This paper proposes a demand-side management policy to coordinate self-interested energy prosumers based on receding horizon games, i.e., a closed-loop receding-horizon implementation of game-theoretic day-ahead planning. Practical stability and recursive constraint satisfaction of the proposed feedback control polic…
Towards bridging classical optimal control and online learning, regret minimization has recently been proposed as a control design criterion. This competitive paradigm penalizes the loss relative to the optimal control actions chosen by a clairvoyant policy, and allows tracking the optimal performance in hindsight no matter how disturbances are generated. In this paper, we propose the first receding horizon scheme based on the repeated computation of finite horizon regret-optimal policies, and we establish stability and safety guarantees for the resulting closed-loop system. Our derivations co…
This paper presents a complementary approach to establish stability of finite receding horizon control with a terminal cost. First a new augmented stage cost is defined by rotating the terminal cost. Then a one-step optimisation problem is defined based on this augmented stage cost. It is shown that a slightly modified Model Predictive Control (MPC) algorithm is stable if the value function of the augmented one-step cost (OSVF) is a control Lyapunov function. The proposed stability condition is completely complementary to the existing terminal cost based MPC stability conditions in the sense t…
We consider the problem of estimating the states of a distributed network of nodes (targets) through a team of cooperating agents (sensors) persistently visiting the nodes so that an overall measure of estimation error covariance evaluated over a finite period is minimized. We formulate this as a multi-agent persistent monitoring problem where the goal is to control each agent's trajectory defined as a sequence of target visits and the corresponding dwell times spent making observations at each visited target. A distributed on-line agent controller is developed where each agent solves a sequen…
This paper proposes a receding horizon active learning and control problem for dynamical systems in which Gaussian Processes (GPs) are utilized to model the system dynamics. The active learning objective in the optimization problem is presented by the exact conditional differential entropy of GP predictions at multiple steps ahead, which is equivalent to the log determinant of the GP posterior covariance matrix. The resulting non-convex and complex optimization problem is solved by the Sequential Convex Programming algorithm that exploits the first-order approximations of non-convex functions.…
A disturbance-aware predictive control policy is proposed for DC-AC power inverters with the receding horizon optimization approach. First, a discrete event-driven hybrid automaton model has been constructed for the nonlinear inverter system dynamics. A control problem of infinite discrete state-space transition sequence optimization is formulated. A receding horizon optimization approach is applied to solve the discrete optimization problem piece-wisely on-line. Accordingly, disturbance-aware adaptive control is proposed, the external disturbance is sampled and estimated by an on-line Recursi…
This paper presents an iterative learning control (ILC) scheme for continuously operated repetitive systems for which no initial condition reset exists. To accomplish this, we develop a lifted system representation that accounts for the effect of the initial conditions on dynamics and projects the dynamics over multiple future iterations. Additionally, we develop an economic cost function and update law that considers the performance over multiple iterations in the future, thus allowing for the prediction horizon to be larger than just the next iteration. Convergence of the iteration varying i…
Receding horizon control (RHC) is a popular procedure to deal with optimal control problems. Due to the existence of state constraints, optimization-based RHC often suffers the notorious issue of infeasibility, which strongly shrinks the region of controllable state. This paper proposes a generalized control barrier function (CBF) to enlarge the feasible region of constrained RHC with only a one-step constraint on the prediction horizon. This design can reduce the constrained steps by penalizing the tendency to move towards the constraint boundary. Additionally, generalized CBF is able to hand…
In this paper, we propose an approach to coordinated receding-horizon control of vehicle speed and transmission gearshift for automated battery electric vehicles (BEVs) to achieve improved energy efficiency. The introduction of multi-speed transmissions in BEVs creates an opportunity to manipulate the operating point of electric motors under given vehicle speed and acceleration command, thus providing the potential to further improve the energy efficiency. However, co-optimization of vehicle speed and transmission gearshift leads to a mixed integer nonlinear program (MINLP), solving which can …
In this article we present a unified framework based on receding horizon techniques that can be used to design the three tasks (guidance, navigation and path-planning) which are involved in the autonomy of unmanned vehicles. This tasks are solved using model predictive control and moving horizon estimation techniques, which allows us to include physical and dynamical constraints at the design stage, thus leading to optimal and feasible results. In order to demonstrate the capabilities of the proposed framework, we have used Gazebo simulator in order to drive a Jackal unmanned ground vehicle (U…
In this paper we provide provable regret guarantees for an online meta-learning receding horizon control algorithm in an iterative control setting. We consider the setting where, in each iteration the system to be controlled is a linear deterministic system that is different and unknown, the cost for the controller in an iteration is a general additive cost function and there are affine control input constraints. By analysing conditions under which sub-linear regret is achievable, we prove that the meta-learning online receding horizon controller achieves an average of the dynamic regret for t…
