This paper studies integral-type event-triggered model predictive control (MPC) of continuous-time nonlinear systems. An integral-type event-triggered mechanism is proposed by incorporating the integral of errors between the actual and predicted state sequences, leading to reduced average sampling frequency. Besides, a new and improved robustness constraint is introduced to handle the additive disturbance, rendering the MPC problem with a potentially enlarged initial feasible region. Furthermore, the feasibility of the designed MPC and the stability of the closed-loop system are rigorously investigated. Several sufficient conditions to guarantee these properties are established, which is related to factors such as the prediction horizon, the disturbance bound, the triggering level, and the contraction rate for the robustness constraint. The effectiveness of the proposed algorithm is illustrated by numerical examples and comparisons.
In this paper we propose a data-driven distributionally robust Model Predictive Control framework for constrained stochastic systems with unbounded additive disturbances. Recursive feasibility is ensured by optimizing over an linearly interpolated initial state constraint in combination with a simplified affine disturbance feedback policy. We consider a moment-based ambiguity set with data-driven radius for the second moment of the disturbance, where we derive a minimum number of samples in order to ensure user-given confidence bounds on the chance constraints and closed-loop performance. The …
A boundary feedback stabilisation problem of non-uniform linear hyperbolic systems of balance laws with additive disturbance is discussed. A continuous and a corresponding discrete Lyapunov function is defined. Using an input-to-state-stability (ISS) $ L^2- $Lyapunov function, the decay of solutions of linear systems of balance laws is proved. In the discrete framework, a first-order finite volume scheme is employed. In such cases, the decay rates can be explicitly derived. The main objective is to prove the Lyapunov stability for the $L^2$-norm for linear hyperbolic systems of balance laws wi…
Nowadays control systems are mostly implemented on digital platforms and, increasingly, over shared communication networks. Reducing resources (processor utilization, network bandwidth, etc.) in such implementations increases the potential to run more applications on the same hardware. We present a self-triggered implementation of linear controllers that reduces the amount of controller updates necessary to retain stability of the closed-loop system. Furthermore, we show that the proposed self-triggered implementation is robust against additive disturbances and provide explicit guarantees of p…
Deep Reinforcement Learning Optimization for Uncertain Nonlinear Systems via Event-Triggered Robust Adaptive Dynamic Programming
Department of Computer Science, University College London（计算机科学系，伦敦大学学院）；Department of Electrical and Electronic Engineering, University of Manchester（电子与电气工程系，曼彻斯特大学）
This paper is concerned with the leader-following consensus problem for a class of Lipschitz nonlinear multi-agent systems with uncertain dynamics, where each agent only transmits its noisy output, at discrete instants and independently from its neighbors. The proposed consensus protocol is based on a continuous-discrete time observer, which provides a continuous time estimation of the state of the neighbors from their discrete-time output measurements, together with a continuous control law. The stability of the multi-agent system is analyzed with a Lyapunov approach and the exponential pract…
In this paper, a self-triggered adaptive model predictive control (MPC) algorithm is proposed for constrained discrete-time nonlinear systems subject to parametric uncertainties and additive disturbances. To bound the parametric uncertainties with reduced overestimation, a zonotope-based set-membership parameter estimator is developed, which is also compatible with the aperiodic sampling resulted from the self-triggering mechanism. The estimation of uncertainties is employed to reformulate the optimization problem in a min-max MPC scheme to reduce the conservatism. By designing a time-varying …
This paper studies the event-triggered cooperative global robust output regulation problem for a class of nonlinear multi-agent systems via a distributed internal model design. We show that our problem can be solved practically in the sense that the ultimate bound of the tracking error can be made arbitrarily small by adjusting a design parameter in the proposed event-triggered mechanism. Our result offers a few new features. First, our control law is robust against both external disturbances and parameter uncertainties, which are allowed to belong to some arbitrarily large prescribed compact …
In this work, we derive a region-based self-triggered control (STC) scheme for nonlinear systems with bounded disturbances and model uncertainties. The proposed STC scheme is able to guarantee different performance specifications (e.g. stability, boundedness, etc.), depending on the event-triggered control (ETC) triggering function that is chosen to be emulated. To deal with disturbances and uncertainties, we employ differential inclusions (DIs). By introducing ETC/STC notions in the context of DIs, we extend well-known results on ETC/STC to perturbed uncertain systems. Given these results, an…
Robust global stabilization of nonlinear systems by observer-based feedback controllers is a challenging task. This article investigates the problem of designing observer-based stabilizing controllers for incrementally quadratic nonlinear systems with external disturbances. The nonlinearities considered in the system model satisfy the incremental quadratic constraints, which are characterized by incremental multiplier matrices and encompass many common nonlinearities. The simultaneous search for the observer and the controller gain matrices is formulated as a feasibility problem of linear matr…
The focus of this paper is on the co-design of control and communication protocol for the control of multiple applications with unknown parameters using a distributed embedded system. The co-design consists of an adaptive switching controller and a hybrid communication architecture that switches between a time-triggered and event-triggered protocol. It is shown that the overall co-design leads to an overall switching adaptive system that has bounded solutions and ensures tracking in the presence of a class of disturbances. In order to achieve the goal of tracking persistent excitation techniqu…
This paper studies periodic event-triggered networked control for nonlinear systems, where the plants and controllers are connected by multiple independent communication channels. Several network-induced imperfections are considered simultaneously, including time-varying inter-sampling times, sensor node scheduling, and especially, large time-varying transmission delays, where the transmitted signal may arrive at the destination node after the next transmission occurs. A new hybrid system approach is provided to model the closed-loop system that contains all communication related behavior. The…
This paper revisits the classical multi-agent average consensus problem for which many different event-triggered control strategies have been proposed over the last decade. Many of the earliest versions of these works conclude asymptotic stability without proving that Zeno behavior, or deadlocks, do not occur along the trajectories of the system. More recent works that resolve this issue either: (i) propose the use of a dwell-time that forces inter-event times to be lower-bounded away from zero but sacrifice asymptotic convergence in exchange for practical convergence (or convergence to a neig…
We present a robust Distributed and Localized Model Predictive Control (rDLMPC) framework for large-scale structured linear systems. The proposed algorithm uses the System Level Synthesis to provide a distributed closed-loop model predictive control scheme that is robust to exogenous disturbances. The resulting controllers require only local information exchange for both synthesis and implementation. We exploit the fact that for polytopic disturbance constraints, SLS- based distributed control problems have been shown to have structure amenable for distributed optimization techniques. We show …
This note describes a reference governor design for a continuous-time nonlinear system with an additive disturbance. The design is based on predicting the response of the nonlinear system by the response of a linear model with a set-bounded prediction error, where a state-and-input dependent bound on the prediction error is explicitly characterized using logarithmic norms. The online optimization is reduced to a convex quadratic program with linear inequality constraints. Two numerical examples are reported.
In this paper, we consider the problem of optimizing the worst-case behavior of a partially observed system. All uncontrolled disturbances are modeled as finite-valued uncertain variables. Using the theory of cost distributions, we present a dynamic programming (DP) approach to compute a control strategy that minimizes the maximum possible total cost over a given time horizon. To improve the computational efficiency of the optimal DP, we introduce a general definition for information states and show that many information states constructed in previous research efforts are special cases of ours…
This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a tractable convex approximation of the optimal covariance steering problem is developed by tightening the chance constraints and by introducing a suitable change of variables. The solution of the convex approximation is shown to be a valid (albeit potentially suboptimal) solution to the original chance-constrained covariance steering problem.
This paper proposes a robust self-triggered distributed model predictive control (DMPC) scheme for a family of Discrete-Time linear systems with local (uncoupled) and global (coupled) constraints. To handle the additive disturbance, tube-based method is proposed for the satisfaction of local state and control constraints. Meanwhile, A special form of constraints tightening is given to guarantee the global coupled constraints. The self-triggering mechanism help reduce the computation burden by skip insignificant iteration steps, which determine a certain sampling instants to solve the DMPC opti…
An optimal control problem with an infinite horizon quadratic cost functional for a linear system with a known additive disturbance is considered. The feature of this problem is that a weight matrix of the control cost in the cost functional is singular. Due to this singularity, the problem can be solved neither by application of the Pontriagin's Maximum Principle, nor using the Hamilton-Jacobi-Bellman equation approach, i.e. this problem is singular. Since the weight matrix of the control cost, being singular, is not in general zero, only a part of the control coordinates is singular, while t…
We introduce a monotonicity-based method for studying input-to-state stability (ISS) of nonlinear parabolic equations with boundary inputs. We first show that a monotone control system is ISS if and only if it is ISS w.r.t. constant inputs. Then we show by means of classical maximum principles that nonlinear parabolic equations with boundary disturbances are monotone control systems. With these two facts, we establish that ISS of the original nonlinear parabolic PDE with constant \textit{boundary disturbances} is equivalent to ISS of a closely related nonlinear parabolic PDE with constant \tex…
The paper considers constrained linear systems with stochastic additive disturbances and noisy measurements transmitted over a lossy communication channel. We propose a model predictive control (MPC) law that minimizes a discounted cost subject to a discounted expectation constraint. Sensor data is assumed to be lost with known probability, and data losses are accounted for by expressing the predicted control policy as an affine function of future observations, which results in a convex optimal control problem. An online constraint-tightening technique ensures recursive feasibility of the onli…
Linear models with additive unknown-but-bounded input disturbances are extensively used to model uncertainty in robust control systems design. Typically, the disturbance set is either assumed to be known a priori or estimated from data through set-membership identification. However, the problem of computing a suitable input disturbance set in case the set of possible output values is assigned a priori has received relatively little attention. This problem arises in many contexts, such as in supervisory control, actuator design, decentralized control, and others. In this paper, we propose a met…
In this paper, we consider the robust closed-loop model predictive control (MPC) of a linear time-variant (LTV) system with norm bounded disturbances and LTV model uncertainty, wherein a series of constrained optimal control problems (OCPs) are solved. Guaranteeing robust feasibility of these OCPs is challenging due to disturbances perturbing the predicted states, and model uncertainty, both of which can render the closed-loop system unstable. As such, a trade-off between the numerical tractability and conservativeness of the solutions is often required. We use the System Level Synthesis (SLS)…
Model Predictive Control is an extremely effective control method for systems with input and state constraints. Model Predictive Control performance heavily depends on the accuracy of the open-loop prediction. For systems with uncertainty this in turn depends on the information that is available about the properties of the model and disturbance uncertainties. Here we are interested in situations where such information is only available through realizations of the system trajectories. We propose a general scenario-based optimization framework for stochastic control of a linear system affected b…
We propose an open loop methodology based on sample statistics to solve chance constrained stochastic optimal control problems with probabilistic safety guarantees for linear systems where the additive Gaussian noise has unknown mean and covariance. We consider a joint chance constraint for time-varying polytopic target sets under assumptions that the disturbance has been sufficiently sampled. We derive two theorems that allow us to bound the probability of the state being more than some number of sample standard deviations away from the sample mean. We use these theorems to reformulate the ch…
For systems with uncertain linear models, bounded additive disturbances and state and control constraints, a robust model predictive control algorithm incorporating online model adaptation is proposed. Sets of model parameters are identified online and employed in a robust tube MPC strategy with a nominal cost. The algorithm is shown to be recursively feasible and input-to-state stable. Computational tractability is ensured by using polytopic sets of fixed complexity to bound parameter sets and predicted states. Convex conditions for persistence of excitation are derived and are related to pro…
This paper studies control synthesis for a general class of nonlinear, control-affine dynamical systems under additive disturbances and state-estimation errors. We enforce forward invariance of static and dynamic safe sets and convergence to a given goal set within a user-defined time in the presence of input constraints. We use robust variants of control barrier functions (CBF) and fixed-time control Lyapunov functions (FxT-CLF) to incorporate a class of additive disturbances in the system dynamics, and state-estimation errors. To solve the underlying constrained control problem, we formulate…
In this paper, we study the robustness of the event-triggered consensus algorithms against frequency-domain uncertainties. It is revealed that the sampling errors resulted by event triggering are essentially images of linear finite-gain $\mathcal{L}_2$-stable operators acting on the consensus errors of the sampled states and the event-triggered mechanism is equivalent to a negative feedback loop introduced additionally to the feedback system. In virtue of this, the robust consensus problem of the event-triggered network systems subject to additive dynamic uncertainties and network multiplicati…
We propose a stochastic MPC scheme using an optimization over the initial state for the predicted trajectory. Considering linear discrete-time systems under unbounded additive stochastic disturbances subject to chance constraints, we use constraint tightening based on probabilistic reachable sets to design the MPC. The scheme avoids the infeasibility issues arising from unbounded disturbances by including the initial state as a decision variable. We show that the stabilizing control scheme can guarantee constraint satisfaction in closed loop, assuming unimodal disturbances. In addition to illu…
Context-Triggered Robust MPC for Temporal Logic Specifications
Max Planck Institute for Software Systems (MPI-SWS)（马克斯·普朗克软件系统研究所）；Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究院）；University of Birmingham（伯明翰大学）
A robust model predictive control (MPC) method is presented for linear, time-invariant systems affected by bounded additive disturbances. The main contribution is the offline design of a disturbance-affine feedback gain whereby the resulting constraint tightening is minimized. This is achieved by formulating the constraint tightening problem as a convex optimization problem with the feedback term as a variable. The resulting MPC controller has the computational complexity of nominal MPC, and guarantees recursive feasibility, stability and constraint satisfaction. The advantages of the proposed…
