3,838 research outputs found
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
Almost sure exponential stabilisation of stochastic systems by state-feedback control
So far, a major part of the literature on the stabilisation issues of stochastic systems has been dedicated to mean square stability. This paper develops a new class of criteria for designing a controller to stabilise a stochastic system almost surely which is unable to be stabilised in mean-square sense. The results are expressed in terms of linear matrix inequalities (LMIs) which are easy to be checked in practice by using MATLAB Toolbox. Moreover, the control structure in this paper appears not only in the drift part but also in the diusion part of the underlying stochastic system
On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach
In this article, we consider a receding horizon control of discrete-time
state-dependent jump linear systems, particular kind of stochastic switching
systems, subject to possibly unbounded random disturbances and probabilistic
state constraints. Due to a nature of the dynamical system and the constraints,
we consider a one-step receding horizon. Using inverse cumulative distribution
function, we convert the probabilistic state constraints to deterministic
constraints, and obtain a tractable deterministic receding horizon control
problem. We consider the receding control law to have a linear state-feedback
and an admissible offset term. We ensure mean square boundedness of the state
variable via solving linear matrix inequalities off-line, and solve the
receding horizon control problem on-line with control offset terms. We
illustrate the overall approach applied on a macroeconomic system
A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information
Copyright q 2012 Hongli Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out. © 2012 Hongli Dong et al.This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of German
Stochastic Asymptotic Stabilizers for Deterministic Input-Affine Systems based on Stochastic Control Lyapunov Functions
In this paper, a stochastic asymptotic stabilization method is proposed for
deterministic input-affine control systems, which are randomized by including
Gaussian white noises in control inputs. The sufficient condition is derived
for the diffucion coefficients so that there exist stochastic control Lyapunov
functions for the systems. To illustrate the usefulness of the sufficient
condition, the authors propose the stochastic continuous feedback law, which
makes the origin of the Brockett integrator become globally asymptotically
stable in probability.Comment: A preliminary version of this paper appeared in the Proceedings of
the 48th Annual IEEE Conference on Decision and Control [14
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