We present a robust synthesis algorithm for uncertain linear time-varying (LTV) systems on finite horizons. The uncertain system is described as an interconnection of a known LTV system and a perturbation. The input-output behavior of the perturbation is specified by time-domain Integral Quadratic Constraints (IQCs). The objective is to synthesize a controller to minimize the worst-case performance. This leads to a non-convex optimization. The proposed approach alternates between an LTV synthesis step and an IQC analysis step. Both induced $\mathcal{L}_2$ and terminal Euclidean norm penalties on output are considered for finite horizon performance. The proposed algorithm ensures that the robust performance is non-increasing at each iteration step. The effectiveness of this method is demonstrated using numerical examples.
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.
System level synthesis is a promising approach that formulates structured optimal controller synthesis problems as convex problems. This work solves the distributed linear-quadratic regulator problem under communication constraints directly in infinite-dimensional space, without the finite-impulse response relaxation common in related work. Our method can also be used to construct optimal distributed Kalman filters with limited information exchange. We combine the distributed Kalman filter with state-feedback control to perform localized LQG control with communication constraints. We provide a…
In networked control systems, often the sensory signals are quantized before being transmitted to the controller. Consequently, performance is affected by the coarseness of this quantization process. Modern communication technologies allow users to obtain resolution-varying quantized measurements based on the prices paid. In this paper, we consider optimal controller synthesis of a Quantized-Feedback Linear-Quadratic-Gaussian (QF-LQG) system where the measurements are to be quantized before being transmitted to the controller. The system is presented with several choices of quantizers, along w…
This paper presents a novel approach to synthesize dual controllers for unknown linear time-invariant systems with the tasks of optimizing a quadratic cost while reducing the uncertainty. To this end, a synthesis problem is defined where the feedback law has to simultaneously gain knowledge of the system and robustly optimize the cost. By framing the problem in a finite horizon setting, the trade-offs arising when the tasks include both identification and control are formally captured in the optimization problem. Results show that efficient exploration strategies are achieved when the structur…
This paper presents a convex optimization-based solution to the design of state-feedback controllers for solving the linear quadratic regulator (LQR) problem of uncertain discrete-time systems with multiplicative noise. To synthesize a tractable solution, the recently developed system level synthesis (SLS) framework is leveraged. It is shown that SLS shifts the controller synthesis task from the design of a robust controller to the design of the entire set-valued closed-loop system responses. To this end, the closed-loop system response is entirely characterized by probabilistic set-valued map…
We present a robust model predictive control method (MPC) for discrete-time linear time-delayed systems with state and control input constraints. The system is subject to both polytopic model uncertainty and additive disturbances. In the proposed method, a time-varying feedback control policy is optimized such that the robust satisfaction of all constraints for the closed-loop system is guaranteed. By encoding the effects of the delayed states and inputs into the feedback policy, we solve the robust optimal control problem in MPC using System Level Synthesis which results in a convex quadratic…
For various typical cases and situations where the formulation results in an optimal control problem, the Linear Quadratic Regulator (LQR) approach and its variants continue to be highly attractive. In certain scenarios, it can happen that some prescribed structural constraints on the gain matrix would arise. Consequently then, the Algebraic Riccati Equation (ARE) is no longer applicable in a straightforward way to obtain the optimal solution. This work presents a rather effective alternative optimization approach based on gradient projection. The utilized gradient is obtained through a data-d…
The behaviour of a stochastic dynamical system may be largely influenced by those low-probability, yet extreme events. To address such occurrences, this paper proposes an infinite-horizon risk-constrained Linear Quadratic Regulator (LQR) framework with time-average cost. In addition to the standard LQR objective, the average one-stage predictive variance of the state penalty is constrained to lie within a user-specified level. By leveraging the duality, its optimal solution is first shown to be stationary and affine in the state, i.e., $u(x,λ^*) = -K(λ^*)x + l(λ^*)$, where $λ^*$ is an optimal …
In this paper, we consider an infinite horizon Linear-Quadratic-Gaussian control problem with controlled and costly measurements. A control strategy and a measurement strategy are co-designed to optimize the trade-off among control performance, actuating costs, and measurement costs. We address the co-design and co-optimization problem by establishing a dynamic programming equation with controlled lookahead. By leveraging the dynamic programming equation, we fully characterize the optimal control strategy and the measurement strategy analytically. The optimal control is linear in the state est…
We address the problem of synthesizing distorting mechanisms that maximize privacy of stochastic dynamical systems. Information about the system state is obtained through sensor measurements. This data is transmitted to a remote station through an unsecured/public communication network. We aim to keep part of the system state private (a private output); however, because the network is unsecured, adversaries might access sensor data and input signals, which can be used to estimate private outputs. To prevent an accurate estimation, we pass sensor data and input signals through a distorting (pri…
A Minimax Linear Quadratic Gaussian Method for Antiwindup Control Synthesis
school of Engineering and Information Technology, University of New South Wales at the Australian Defence Force Academy（新南威尔士大学澳大利亚国防学院工程与信息科技学院）；department of Mechanical and Mechatronics Engineering, University of Waterloo（滑铁卢大学机械与机电工程系）
We present SySCoRe, a MATLAB toolbox that synthesizes controllers for stochastic continuous-state systems to satisfy temporal logic specifications. Starting from a system description and a co-safe temporal logic specification, SySCoRe provides all necessary functions for synthesizing a robust controller and quantifying the associated formal robustness guarantees. It distinguishes itself from other available tools by supporting nonlinear dynamics, complex co-safe temporal logic specifications over infinite horizons and model-order reduction. To achieve this, SySCoRe generates a finite-state abs…
In this paper, we study the effect of non-vanishing disturbances on the stability of fixed-time stable (FxTS) systems. We present a new result on FxTS, which allows a positive term in the time derivative of the Lyapunov function with the aim to model bounded, non-vanishing disturbances in the system dynamics. We characterize the neighborhood to which the system trajectories converge, as well the time of convergence to this neighborhood, in terms of the positive and negative terms that appear in the time derivative of the Lyapunov function. Then, we use the new FxTS result and formulate a quadr…
In this work, we propose a compositional scheme for the safety controller synthesis of interconnected discrete-time stochastic systems with Markovian switching signals. Our proposed approach is based on a notion of so-called control storage certificates computed for individual subsystems, by leveraging which, one can synthesize state-feedback controllers for interconnected systems to enforce safety specifications over finite time horizons. To do so, we employ a sum-of-squares (SOS) optimization approach to search for multiple storage certificates of each switching subsystem while synthesizing …
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" …
The goal of Inverse Optimal Control (IOC) is to identify the underlying objective function based on observed optimal trajectories. It provides a powerful framework to model expert's behavior, and a data-driven way to design an objective function so that the induced optimal control is adapted to a contextual environment. In this paper, we design an IOC algorithm for linear-quadratic tracking problems with random time horizon, and prove the statistical consistency of the algorithm. More specifically, the proposed estimator is the solution to a convex optimization problem, which means that the es…
Ensuring nominal asymptotic stability of the Nonlinear Model Predictive Control controller is not trivial. Stabilizing ingredients such as terminal penalty term and terminal region are crucial in establishing the asymptotic stability. Current work presents alternate approaches namely arbitrary controller based approach and linear quadratic regulator based approach, which provide larger degrees of freedom for enlarging the terminal region as against conservative approaches from the literature. Efficacy of the proposed approaches is demonstrated using benchmark two state continuous stirrer tank …
In the past couple of decades, non-quadratic convex penalties have reshaped signal processing and machine learning; in robust control, however, general convex costs break the Riccati and storage function structure that make the design tractable. Practitioners thus default to approximations, heuristics or robust model predictive control that are solved online for short horizons. We close this gap by extending $H_\infty$ control of discrete-time linear systems to strictly convex penalties on state, input, and disturbance, recasting the objective with Bregman divergences that admit a completion-o…
We present a convex solution for the design of generalized accelerated gradient algorithms for strongly convex objective functions with Lipschitz continuous gradients. We utilize integral quadratic constraints and the Youla parameterization from robust control theory to formulate a solution of the algorithm design problem as a convex semi-definite program. We establish explicit formulas for the optimal convergence rates and extend the proposed synthesis solution to extremum control problems.
We consider a discrete-time linear-quadratic Gaussian control problem in which we minimize a weighted sum of the directed information from the state of the system to the control input and the control cost. The optimal control and sensing policies can be synthesized jointly by solving a semidefinite programming problem. However, the existing solutions typically scale cubic with the horizon length. We leverage the structure in the problem to develop a distributed algorithm that decomposes the synthesis problem into a set of smaller problems, one for each time step. We prove that the algorithm ru…
RWTH Aachen University（亚琛工业大学）；Ingenieurgesellschaft Auto und Verkehr (IAV)（IAV汽车与交通工程公司）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. While learning-based control has the potential to yield superior performance in demanding applications, robustness to uncertainty remains an important challenge. Since Bayesian methods quantify uncertainty of the learning results, it is natural to incorporate these uncertainties into a robust design. In contrast to most state-of-the-art approaches that consider worst-case estimates, we leverage the learning method's posterior distribution i…
System Level Synthesis (SLS) parametrization facilitates controller synthesis for large, complex, and distributed systems by incorporating system level constraints (SLCs) into a convex SLS problem and mapping its solution to stable controller design. Solving the SLS problem at scale efficiently is challenging, and current attempts take advantage of special system or controller structures to speed up the computation in parallel. However, those methods do not generalize as they rely on the specific system/controller properties. We argue that it is possible to solve general SLS problems more effi…
In this work, we consider the problem of regret minimization in adaptive minimum variance and linear quadratic control problems. Regret minimization has been extensively studied in the literature for both types of adaptive control problems. Most of these works give results of the optimal rate of the regret in the asymptotic regime. In the minimum variance case, the optimal asymptotic rate for the regret is $\log(T)$ which can be reached without any additional external excitation. On the contrary, for most adaptive linear quadratic problems, it is necessary to add an external excitation in orde…
