Almost Sure Stabilization for Adaptive Controls of Regime-switching LQ Systems with A Hidden Markov Chain

This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a hidden Markov chain. Different from previous work on stabilization of adaptive controlled systems with a hidden Markov chain, where average criteria were considered, this work focuses on the almost sure stabilization or sample path stabilization of the underlying processes. Under simple conditions, it is shown that as long as the feedback controls have linear growth in the continuous component, the resulting process is regular. Moreover, by appropriate choice of the Lyapunov functions, it is shown that the adaptive system is stabilizable almost surely. As a by-product, it is also established that the controlled process is positive recurrent

Global stabilization of linear systems with bounds on the feedback and its successive derivatives

We address the global stabilization of linear time-invariant (LTI) systems when the magnitude of the control input and its successive time derivatives, up to an order $p\in\mathbb N$, are bounded by prescribed values. We propose a static state feedback that solves this problem for any admissible LTI systems, namely for stabilizable systems whose internal dynamics has no eigenvalue with positive real part. This generalizes previous work done for single-input chains of integrators and rotating dynamics

Output feedback stable stochastic predictive control with hard control constraints

We present a stochastic predictive controller for discrete time linear time invariant systems under incomplete state information. Our approach is based on a suitable choice of control policies, stability constraints, and employment of a Kalman filter to estimate the states of the system from incomplete and corrupt observations. We demonstrate that this approach yields a computationally tractable problem that should be solved online periodically, and that the resulting closed loop system is mean-square bounded for any positive bound on the control actions. Our results allow one to tackle the largest class of linear time invariant systems known to be amenable to stochastic stabilization under bounded control actions via output feedback stochastic predictive control

Stabilization of positive linear continuous-time systems by using a Brauer´s theorem

[EN] In this paper we study the stability property of positive linear continuous-time systems. This property is useful to study the asymptotic behavior of a dynamical system and specifically, in positive systems. Stabilization of linear systems using feedbacks has been deeply studied during the last decades. Motivated by some results, in this paper we find conditions on the system such that the eigenvalues of the closed loop system are in the open left half plane of the complex plane C. We do this by applying a Brauer s theorem.The authors would like to thank the referees and the editor for their comments and useful suggestions for improvement of the manuscript. This research was partially supported by Spanish Grant MTM2013-43678-P.Cantó Colomina, B.; Cantó Colomina, R.; Urbano Salvador, AM. (2016). Stabilization of positive linear continuous-time systems by using a Brauer´s theorem. International Journal of Complex Systems in Science. 6(1):23-28. http://hdl.handle.net/10251/81742S23286

Phase-locked scroll waves defy turbulence induced by negative filament tension

Scroll waves in a three-dimensional media may develop into turbulence due to negative tension of the filament. Such negative tension-induced instability of scrollwaves has been observed in the Belousov-Zhabotinsky reaction systems. Here we propose a method to restabilize scroll wave turbulence caused by negative tension in three-dimensional chemical excitable media using a circularly polarized (rotating) external field. The stabilization mechanism is analyzed in terms of phase-locking caused by the external field, which makes the effective filament tension positive. The phase-locked scrollwaves that have positive tension and higher frequency defy the turbulence and finally restore order. A linear theory for the change of filament tension caused by a generic rotating external field is presented and its predictions closely agree with numerical simulations