Packetized Predictive Control for Rate-Limited Networks via Sparse Representation

We study a networked control architecture for linear time-invariant plants in which an unreliable data-rate limited network is placed between the controller and the plant input. The distinguishing aspect of the situation at hand is that an unreliable data-rate limited network is placed between controller and the plant input. To achieve robustness with respect to dropouts, the controller transmits data packets containing plant input predictions, which minimize a finite horizon cost function. In our formulation, we design sparse packets for rate-limited networks, by adopting an an ell-0 optimization, which can be effectively solved by an orthogonal matching pursuit method. Our formulation ensures asymptotic stability of the control loop in the presence of bounded packet dropouts. Simulation results indicate that the proposed controller provides sparse control packets, thereby giving bit-rate reductions for the case of memoryless scalar coding schemes when compared to the use of, more common, quadratic cost functions, as in linear quadratic (LQ) control.Comment: 9 pages, 7 figures. arXiv admin note: text overlap with arXiv:1307.824

Sparse Packetized Predictive Control for Networked Control over Erasure Channels

We study feedback control over erasure channels with packet-dropouts. To achieve robustness with respect to packet-dropouts, the controller transmits data packets containing plant input predictions, which minimize a finite horizon cost function. To reduce the data size of packets, we propose to adopt sparsity-promoting optimizations, namely, ell-1-ell-2 and ell-2-constrained ell-0 optimizations, for which efficient algorithms exist. We derive sufficient conditions on design parameters, which guarantee (practical) stability of the resulting feedback control systems when the number of consecutive packet-dropouts is bounded.Comment: IEEE Transactions on Automatic Control, Volume 59 (2014), Issue 7 (July) (to appear

Sparse and Constrained Stochastic Predictive Control for Networked Systems

This article presents a novel class of control policies for networked control of Lyapunov-stable linear systems with bounded inputs. The control channel is assumed to have i.i.d. Bernoulli packet dropouts and the system is assumed to be affected by additive stochastic noise. Our proposed class of policies is affine in the past dropouts and saturated values of the past disturbances. We further consider a regularization term in a quadratic performance index to promote sparsity in control. We demonstrate how to augment the underlying optimization problem with a constant negative drift constraint to ensure mean-square boundedness of the closed-loop states, yielding a convex quadratic program to be solved periodically online. The states of the closed-loop plant under the receding horizon implementation of the proposed class of policies are mean square bounded for any positive bound on the control and any non-zero probability of successful transmission

Maximum Hands-Off Control: A Paradigm of Control Effort Minimization

In this paper, we propose a new paradigm of control, called a maximum hands-off control. A hands-off control is defined as a control that has a short support per unit time. The maximum hands-off control is the minimum support (or sparsest) per unit time among all controls that achieve control objectives. For finite horizon control, we show the equivalence between the maximum hands-off control and L1-optimal control under a uniqueness assumption called normality. This result rationalizes the use of L1 optimality in computing a maximum hands-off control. We also propose an L1/L2-optimal control to obtain a smooth hands-off control. Furthermore, we give a self-triggered feedback control algorithm for linear time-invariant systems, which achieves a given sparsity rate and practical stability in the case of plant disturbances. An example is included to illustrate the effectiveness of the proposed control.Comment: IEEE Transactions on Automatic Control, 2015 (to appear

Stochastic model predictive control for constrained networked control systems with random time delay

In this paper the continuous time stochastic constrained optimal control problem is formulated for the class of networked control systems assuming that time delays follow a discrete-time, finite Markov chain . Polytopic overapproximations of the system's trajectories are employed to produce a polyhedral inner approximation of the non-convex constraint set resulting from imposing the constraints in continuous time. The problem is cast in a Markov jump linear systems (MJLS) framework and a stochastic MPC controller is calculated explicitly, oine, coupling dynamic programming with parametric piecewise quadratic (PWQ) optimization. The calculated control law leads to stochastic stability of the closed loop system, in the mean square sense and respects the state and input constraints in continuous time