Detector-based <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml17" display="inline" overflow="scroll" altimg="si4.gif"><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math> results for discrete-time Markov jump linear systems with partial observations

Summary The scriptH2, scriptH∞ and mixed scriptH2false/scriptH∞ dynamic output feedback control of Markov jump linear systems in a partial observation context is studied through an iterative approach. By partial information, we mean that neither the state variable x(k) nor the Markov chain θ(k) are available to the controller. Instead, we assume that the controller relies only on an output y(k) and a measured variable trueθ^false(kfalse) coming from a detector that provides the only information of the Markov chain θ(k). To solve the problem, we resort to an iterative method that starts with a state‐feedback controller and solves at each iteration a linear matrix inequality optimization problem. It is shown that this iterative algorithm yields to a nonincreasing sequence of upper bound costs so that it converges to a minimum value. The effectiveness of the iterative procedure is illustrated by means of two examples in which the conservatism between the upper bounds and actual costs is significantly reduced.

Section: Preliminariesmentioning

confidence: 99%

“…We now introduce the following notation,

{scriptW}_{i} ≜ false{w \in l_{2}^{r}; false‖ w {false‖}_{2, i} > 0 false}

, and for any signal

g = false{g false(k false), k = 0, 1, 2, … false} \in l_{2}^{t}

false‖ g {false‖}_{2, i} ≜ \sqrt{\sum_{k = 0}^{\infty} boldE false(false‖ g false(k false) {false‖}^{2} false| θ_{0} = i false)}

. The following definition of the

{scriptH}_{\infty}

norm of is adapted from the work of Todorov et al…”

Section: Preliminariesmentioning

confidence: 99%

“…We now present a nondegenerescence assumption on the transition probability matrix

double-struckP

. This is a technical restriction needed for the bounded‐real lemma presented in Theorem below, as required by Todorov et al, that is also used in chapter 8 of the work of Dragan et al…”

Section: Preliminariesmentioning

confidence: 99%

“…The following definition of the  ∞ norm of (4) is adapted from the work of Todorov et al 25 Definition 4 ( ∞ norm). Consider that system (4) is SS.…”

Section: Preliminariesmentioning

confidence: 99%

“…The following bounded-real lemma is adapted from theorem 7 of Todorov et al 25 Theorem 1. For a given ∞ > 0, consider the following statements.…”

Section: Preliminariesmentioning

confidence: 99%

See 3 more Smart Citations

An iterative approach for the discrete‐time dynamic control of Markov jump linear systems with partial information

Oliveira

Costa

2019

Asynchronous control for two‐dimensional hidden Markovian jump systems with partly known mode observation conditional probabilities

Zhu

Dullerud

2020

This study focuses on the asynchronous  ∞ control problem for two-dimensional discrete-time hidden Markovian jump systems where the mode observation conditional probability matrix is partly known. Considering the original system modes are invisible, the observed modes emitted from an observer serve as an alternative for stability analysis and controller design where a mode observation conditional probability matrix is constructed to characterize the emission between system modes and observed modes. Specially, only partly known information of the mode observation conditional probability matrix is accessible. With the introduction of the free-connection weighting matrices, the asymptotic mean square stability criterion is firstly derived based on Lyapunov method. This introduction provides a further degree of relaxation and less conservatism is therefore achieved. Secondly, we present synthesis conditions for asynchronous  ∞ state feedback controller design given in terms of a set of interconnected linear matrix inequalities. Moreover, cluster concept based on the partitions of observed modes is adopted which helps to decrease the number of controllers and simplify the design complexity. A numerical example, regarding the cases with and without clustering of the observed modes, is presented to illustrate the effectiveness of the proposed method.

HMM‐based H_∞ filtering for Markov jump systems with partial information and sensor nonlinearities

Zheng

2020

This work examines the H ∞ filtering issue for Markov jump systems in the circumstances of partial information on Markov chain and randomly occurring sensor nonlinearities. The partial information considered in this work includes partial information on the Markov state, on transition probabilities and on detection probabilities. A hidden Markov model with partially known transition probabilities and detection probabilities is introduced to describe the above partial information phenomenon. The randomly occurring sensor nonlinearities considered in this work depend on the system operating mode. Based on the Lyapunov methodology and the introduced hidden Markov model, some effective H ∞ performance analysis criteria are derived for the filtering error system under the circumstances of partial information and sensor nonlinearities. In addition, the design procedure of the desired hidden Markov model-based filter is established, and finally two examples are used to verify the theoretical results.