The goal of this paper is to obtain online abstractions for coupled multi-agent systems in a decentralized manner. A discrete model which captures the motion capabilities of each agent is derived over a bounded time-horizon, by discretizing a corresponding overapproximation of the agent's reachable states. The individual abstractions' composition provides a correct representation of the coupled continuous system over the horizon and renders the approach appropriate for control synthesis under high-level specifications which are assigned to the agents over this time window. Sufficient conditions are also provided for the space and time discretization to guarantee the derivation of deterministic abstractions with tunable transition capabilities.
This paper introduces a data-based moving horizon estimation (MHE) scheme for linear time-invariant discrete-time systems. The scheme solely relies on collected data without employing any system identification step. Robust global exponential stability of the data-based MHE is proven under standard assumptions for the case where the online output measurements are corrupted by some non-vanishing measurement noise. A simulation example illustrates the behavior of the data-based MHE scheme.
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）
This paper presents a novel set-based model predictive control for tracking, which provides the largest domain of attraction, even with the minimal predictive/control horizon. The formulation - which consists of a single optimization problem - shows a dual behavior: one operating inside the maximal controllable set to the feasible equilibrium set, and the other operating at the N-controllable set to the same equilibrium set. Based on some finite-time convergence results, asymptotic stability of the resulting closed-loop is proved, while recursive feasibility is ensured for any change of the se…
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…
We investigate the problem of persistent monitoring, where a mobile agent has to survey multiple targets in an environment in order to estimate their internal states. These internal states evolve with linear stochastic dynamics and the agent can observe them with a linear observation model. However, the signal to noise ratio is a monotonically decreasing function of the distance between the agent and the target. The goal is to minimize the uncertainty in the state estimates over the infinite horizon. We show that, for a periodic trajectory with fixed cycle length, the problem can be formulated…
In many applications of optimal control, the stage cost is not fixed, but rather a design choice with considerable impact on the control performance. In infinite horizon optimal control, the choice of stage cost is often restricted by the requirement of uniform cost controllability, which is nontrivial to satisfy. Here we revisit a previously proposed constructive technique for stage cost design. We generalize its setting, weaken the required assumptions and add additional flexibility. Furthermore, we show that the required assumptions essentially cannot be weakened anymore. By providing impro…
Ensuring nominal asymptotic stability of the Non-linear Model Predictive Control (NMPC) controller is not trivial. Stabilizing ingredients such as terminal penalty term and terminal region are crucial in establishing the asymptotic stability. Approaches available in the literature provide limited degrees of freedom for the characterization of the terminal region for the discrete time Quasi Infinite Horizon NMPC (QIH-NMPC) formulation. Current work presents alternate approaches namely arbitrary controller based approach and LQR based approach, which provide large degrees of freedom for enlargin…
In this paper, we consider the problem of computing parameters of an objective function for a discrete-time optimal control problem from state and control trajectories with active control constraints. We propose a novel method of inverse optimal control that has a computationally efficient online form in which pairs of states and controls from given state and control trajectories are processed sequentially without being stored or processed in batches. We establish conditions guaranteeing the uniqueness of the objective-function parameters computed by our proposed method from trajectories with …
On finite-horizon approximation of an infinite-horizon feedback Nash equilibrium in discrete-time LQ games
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）；School of Economics and Management, China University of Petroleum-Beijing（中国石油大学（北京）经济管理学院）；Department of Mechanics and Engineering Science, Peking University（北京大学力学与工程科学系）
An optimal control law for networked control systems with a discrete-time linear time-invariant (LTI) system as plant and networks between sensor and controller as well as between controller and actuator is proposed. This controller is designed by solving an optimization problem that is a generalization of the optimization problem used to obtain the Linear Quadratic Regulator (LQR) for deterministic discrete-time LTI systems. The networks are represented by random delays and drop outs of transmitted data packets.
The turnpike property refers to the phenomenon that in many optimal control problems, the solutions for different initial conditions and varying horizons approach a neighborhood of a specific steady state, then stay in this neighborhood for the major part of the time horizon, until they may finally depart. While early observations of the phenomenon can be traced back to works of Ramsey and von Neumann on problems in economics in 1928 and 1938, the turnpike property received continuous interest in economics since the 1960s and recent interest in systems and control. The present chapter provides…
The inverse linear-quadratic optimal control problem is a system identification problem whose aim is to recover the quadratic cost function and hence the closed-loop system matrices based on observations of optimal trajectories. In this paper, the discrete-time, finite-horizon case is considered, where the agents are also assumed to be homogeneous and indistinguishable. The latter means that the agents all have the same dynamics and objective functions and the observations are in terms of "snap shots" of all agents at different time instants, but what is not known is "which agent moved where" …
In this paper we study reachability verification problems of stochastic discrete-time dynamical systems over the infinite time horizon. The reachability verification of interest in this paper is to certify specified lower and upper bounds of the reachability probability, with which the system starting from a designated initial set will enter a desired target set eventually. Existing sufficient conditions for reachability verification over the infinite time horizon are established based on the Doob's non-supermartingle inequality, which are often restrictive. Recently, a set of equations was pr…
In this paper, model predictive control (MPC) strategies are proposed for dead-beat control of linear systems with and without state and control constraints. In unconstrained MPC, deadbeat performance can be guaranteed by setting the control horizon to the system dimension, and adding an terminal equality constraint. It is proved that the unconstrained deadbeat MPC is equivalent to linear deadbeat control. The proposed constrained deadbeat MPC is designed by setting the control horizon equal to the system dimension and penalizing only the terminal cost. The recursive feasibility and deadbeat p…
In this work, we consider the problem of steering the first two moments of the uncertain state of a discrete time nonlinear stochastic system to prescribed goal quantities at a given final time. In principle, the latter problem can be formulated as a density tracking problem, which seeks for a feedback policy that will keep the probability density function of the state of the system close, in terms of an appropriate metric, to the goal density. The solution to the latter infinite-dimensional problem can be, however, a complex and computationally expensive task. Instead, we propose a more tract…
