This paper presents a quasi time optimal receding horizon control algorithm. The proposed algorithm generates near time optimal control when the state of the system is far from the target. When the state attains a certain neighbourhood of the aim, it begins the adaptation of the cost function. The purpose of this adaptation is to move from the time optimal control to the stabilizing control. Sufficient conditions for the stability of the closed loop system and the manner of the adaptation of the cost function have been given. Considerations are illustrated with examples.
Keywords: Receding horizon control ;predictive control; nonlinear stability; optimal control.
In this paper we address the problem of designing receding horizon control algorithms for linear discrete-time systems with parametric uncertainty. We do not consider presence of stochastic forcing or process noise in the system. It is assumed that the parametric uncertainty is probabilistic in nature with known probability density functions. We use generalized polynomial chaos theory to design the proposed stochastic receding horizon control algorithms. In this framework, the stochastic problem is converted to a deterministic problem in higher dimensional space. The performance of the propose…
We provide a solution to the problem of receding horizon control for stochastic discrete-time systems with bounded control inputs and imperfect state measurements. For a suitable choice of control policies, we show that the finite-horizon optimization problem to be solved on-line is convex and successively feasible. Due to the inherent nonlinearity of the feedback loop, a slight extension of the Kalman filter is exploited to estimate the state optimally in mean-square sense. We show that the receding horizon implementation of the resulting control policies renders the state of the overall syst…
In this paper, based on real-time nonlinear receding horizon control methodology, a novel approach is developed for parameter estimation of time invariant and time varying nonlinear dynamical systems in chaotic environments. Here, the parameter estimation problem is converted into a family of finite horizon optimization control problems. The corresponding receding horizon control problem is then solved numerically, in real-time, without recourse to any iterative approximation methods by introducing the stabilized continuation method and backward sweep algorithm. The significance of this work l…
Control of stochastic interacting particle systems is a non-trivial task due to the high dimensionality of the problem and the lack of fast algorithms. Here, we propose a space mapping-based approximation of the stochastic control problem by solutions of the deterministic one. In combination with the receding horizon control technique this yields a reliable and fast numerical scheme for the closed loop control of stochastic interacting particle systems. As a numerical example we consider the herding of sheep with dogs. The numerical results underline the feasibility of our approach and further…
This paper investigates the consensus problem of general linear multi-agent systems under the framework of optimization. A novel distributed receding horizon control (RHC) strategy for consensus is proposed. We show that the consensus protocol generated by the unconstrained distributed RHC can be expressed in an explicit form. Based on the resulting consensus protocol the necessary and sufficient conditions for ensuring consensus are developed. Furthermore, we specify more detailed consensus conditions for multi-agent system with general and one-dimensional linear dynamics depending on the dif…
Optimal control problems with a very large time horizon can be tackled with the Receding Horizon Control (RHC) method, which consists in solving a sequence of optimal control problems with small prediction horizon. The main result of this article is the proof of the exponential convergence (with respect to the prediction horizon) of the control generated by the RHC method towards the exact solution of the problem. The result is established for a class of infinite-dimensional linear-quadratic optimal control problems with time-independent dynamics and integral cost. Such problems satisfy the tu…
The Receding Horizon Control (RHC) strategy consists in replacing an infinite-horizon stabilization problem by a sequence of finite-horizon optimal control problems, which are numerically more tractable. The dynamic programming principle ensures that if the finite-horizon problems are formulated with the exact value function as a terminal penalty function, then the RHC method generates an optimal control. This article deals with the case where the terminal cost function is chosen as a cut-off Taylor approximation of the value function. The main result is an error rate estimate for the control …
This work considers the stability of nonlinear stochastic receding horizon control when the optimal controller is only computed approximately. A number of general classes of controller approximation error are analysed including deterministic and probabilistic errors and even controller sample and hold errors. In each case, it is shown that the controller approximation errors do not accumulate (even over an infinite time frame) and the process converges exponentially fast to a small neighbourhood of the origin. In addition to this analysis, an approximation method for receding horizon optimal c…
In control and engineering community, models generally contain a number of parameters which are unknown or roughly known. A complete knowledge of these parameters is critical to describe and analyze the dynamics of the system. This paper develops a novel approach of estimating unknown time-varying parameters of nonlinear systems based on real-time nonlinear receding horizon control strategy. For this purpose, the problem of estimation is converted into optimization problem which can be solved by backwards sweep Riccati method. Methodology is implemented on two nonlinear examples without provid…
This paper presents a novel framework which combines a non-iterative solution of Real-Time Nonlinear Receding Horizon Control (NRHC) methodology to achieve consensus within complex network topologies with existing time-delays and in presence of switching topologies. In this formulation, we solve the distributed nonlinear optimization problem for multi-agent network systems directly, \emph{in real-time}, without any dependency on iterative processes, where the stability and convergence guarantees are provided for the solution. Three benchmark examples on non-linear chaotic systems provide valid…
This paper presents an optimization-based receding horizon trajectory planning algorithm for dynamical systems operating in unstructured and cluttered environments. The proposed approach is a two-step procedure that uses a motion planning algorithm in a first step to efficiently find a feasible, but possibly suboptimal, nominal solution to the trajectory planning problem where in particular the combinatorial aspects of the problem are solved. The resulting nominal trajectory is then improved in a second optimization-based receding horizon planning step which performs local trajectory refinemen…
Platoon formation with connected and automated vehicles (CAVs) in a mixed traffic environment poses significant challenges due to the presence of human-driven vehicles (HDVs) with unknown dynamics and control actions. In this paper, we develop a safety-prioritized receding horizon control framework for creating platoons of HDVs preceded by a CAV. Our framework ensures indirect control of the following HDVs by directly controlling the leading CAV given the safety constraints. The framework utilizes a data-driven prediction model that is based on the recursive least squares algorithm and the con…
Generalized Polynomial Chaos (gPC) theory has been widely used for representing parametric uncertainty in a system, thanks to its ability to propagate uncertainty evolution. In an optimal control context, gPC can be combined with several optimization techniques to achieve a control policy that handles effectively this type of uncertainty. Such a suitable method is Differential Dynamic Programming (DDP), leading to an algorithm that inherits the scalability to high-dimensional systems and fast convergence nature of the latter. In this paper, we expand this combination aiming to acquire probabil…
Microorganisms have developed complex regulatory features controlling their reaction and internal adaptation to changing environments. When modeling these organisms we usually do not have full understanding of the regulation and rely on substituting it with an optimization problem using a biologically reasonable objective function. The resulting constraint-based methods like the Flux Balance Analysis (FBA) and Resource Balance Analysis (RBA) have proven to be powerful tools to predict growth rates, by-products, and pathway usage for fixed environments. In this work, we focus on the dynamic enz…
We present a method for simultaneous Receding Horizon Estimation and Control of a robotic arm equipped with a sword in an adversarial situation. Using a single camera mounted on the arm, we solve the problem of blocking a opponent's sword with the robot's sword. Our algorithm uses model-based sensing to estimate the opponent's intentions from the camera's observations, while it simultaneously applies a control action to both block the opponent's sword and improve future camera observations.
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.
An increasing number of control techniques are introduced to HIV infection problem to explore the options of helping clinical testing, optimizing drug treatments and to study the drug resistance situations. In such cases, complete/accurate knowledge of the HIV model and/or parameters is critical not only to monitor the dynamics of the system, but also to adjust the therapy accordingly. In those studies, existence of any type of unknown parameters imposes severe set-backs and becomes problematic for the treatment of the patients. In this work, we develop a real-time adaptive nonlinear receding …
It is desirable but challenging to fulfill system constraints and reach optimal performance in consensus protocol design for practical multi-agent systems (MASs). This paper investigates the optimal consensus problem for general linear MASs subject to control input constraints. Two classes of MASs including subsystems with semi-stable and unstable dynamics are considered. For both classes of MASs without input constraints, the results on designing optimal consensus protocols are first developed by inverse optimality approach. Utilizing the optimal consensus protocols, the receding horizon cont…
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…
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…
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…
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 …
Decoding of convolutional codes poses a significant challenge for coding theory. Classical methods, based on e.g. Viterbi decoding, suffer from being computationally expensive and are restricted therefore to codes of small complexity. Based on analogies with model predictive optimal control, we propose a new iterative method for convolutional decoding that is cheaper to implement than established algorithms, while still offering significant error correction capabilities. The algorithm is particularly well-suited for decoding special types of convolutional codes, such as e.g. cyclic convolution…
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…
Receding-Horizon Policy Gradient for Polytopic Controller Synthesis
William E. Boeing Department of Aeronautics and Astronautics, University of Washington（华盛顿大学威廉E.波音航空航天系）；Corvinus Institute for Advanced Studies (CIAS)（科尔维努斯高级研究院）；Institute of Data Analytics and Information Systems, Corvinus University of Budapest（布达佩斯科尔维努斯大学数据分析和信息系统研究所）；Hungarian Research Network (HUN-REN)（匈牙利研究网络）
The present work is concerned with the stabilization of a general class of time-varying linear parabolic equations by means of a finite-dimensional receding horizon control (RHC). The stability and suboptimality of the unconstrained receding horizon framework is studied. The analysis allows the choice of the squared $\ell_1$-norm as control cost. This leads to a nonsmooth infinite-horizon problem which provides stabilizing optimal controls with a low number of active actuators over time. Numerical experiments are given which validate the theoretical results and illustrate the qualitative diffe…
This paper proposes a hierarchical decentralized reference governor for constrained cascade systems. The reference governor (RG) approach is reformulated in terms of receding horizon strategy such that a locally receding horizon optimization is obtained for each subsystem with a pre-established prediction horizon. The algorithm guarantees that not only the nominal overall closed-loop system without any constraint is recoverable but also the state and control constraints are satisfied in transient conditions. Also, considering unfeasible reference signals, the output of any subsystem goes local…
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 describes a method for scheduling the events of a switched system to achieve an optimal performance. The approach has guarantees on convergence and computational complexity that parallel derivative-based iterative optimization but in the infinite dimensional, integer constrained setting of mode scheduling. In comparison to methods relying on mixed integer programming, the presented approach does not require a priori discretizations of time or state. Furthermore, in comparison to embedding and relaxation methods, every iteration of the algorithm returns a dynamically feasible solutio…
