This paper addresses the problem of identifying linear multi-variable models from the inputoutput data which is corrupted by an unknown, non-centered, and sparse vector error sequence. This problem is sometimes referred to as error correcting problem in coding theory and robust estimation problem in statistics. By taking advantage of some recent developments in sparse optimization theory, we present here a recursive approach. We then show that the proposed identification method can be adapted to estimate parameter matrices of Jump Markov Linear Systems (JMLS), that is, switched linear systems in which the discrete state sequence is a stationary Markov chain. Some numerical simulation results illustrate the potential of the new method.
This paper addresses the problem of driving the state of a linear discrete-time system to zero in minimum time. The inputs are constrained to lie in a bounded and convex set. The solution presented in the paper is based on the observation that the state sequence induced by the minimum-time control sequence is the sparsest possible state sequence over a certain finite horizon. That is, the desired state sequence must contain as many zero vectors as possible, all those zeros corresponding to the highest values of the time index. Hence, by taking advantage of some recent developments in sparse optimization theory, we propose a numerical solution. We show in simulation that the proposed method can effectively solve the minimumtime problem even for multi-inputs linear discrete-time systems.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.