H∞ Control for Continuous‐Time Mean‐Field Stochastic Systems

An H_∞‐type control is considered for mean‐field stochastic differential equations (SDEs) in this paper. A stochastic bounded real lemma (SBRL) is proved for mean‐field stochastic continuous‐time systems with state‐ and disturbance‐dependent noise. Based on SBRL, a sufficient condition is given for the existence of a stabilizing H_∞ controller in terms of coupled nonlinear matrix inequalities.     

Output Feedback H∞ Control for Discrete‐time Mean‐field Stochastic Systems

This paper is to consider dynamic output feedback H_∞ control of mean‐field type for stochastic discrete‐time systems with state‐ and disturbance‐dependent noise. A stochastic bounded real lemma (SBRL) of mean‐field type is derived. Based on the SBRL, a sufficient condition with the form of coupled nonlinear matrix inequalities is derived for the existence of a stabilizing H_∞ controller. Moreover, a numerical example is given to examine the effectiveness of the theoretical results.     

Necessary and Sufficient Near‐Optimal Conditions for Mean‐Field Singular Stochastic Controls

We consider the near‐optimal control problems for mean‐field singular stochastic systems, where the control domain is non‐convex. By virtue of Ekeland's principle and some estimates on the state and adjoint processes, necessary and sufficient conditions for near‐optimality are established in the mean‐field framework. As an application, an example is presented to demonstrate the results.     

Robust H∞ Filtering For Uncertain Stochastic Time‐Delay Systems

This paper deals with the problem of robust H_∞ filtering for uncertain stochastic systems. The system under consideration is subject to time‐varying norm‐bounded parameter uncertainties and unknown time delays in both the state and measurement equations. The problem we address is the design of a stable filter that ensures the robust stochastic stability and a prescribed H_∞ performance level for the filtering error system irrespective of all admissible uncertainties and time delays. A suffient condition for the solvability of this problem is proposed and a linear matrix inequality approach is developed for the design of the robust H_∞ filters. An illustrative example is provided to demonstrate the effctiveness of the proposed approach.     

Reset Control Systems With Time‐Varying Delay: Delay‐Dependent Stability And Gain Performance Improvement

This paper considers the stability analysis of reset control systems with time‐varying delay. Based on sector reset conditions, delay‐dependent exponential stability and finite gain stability conditions are proposed, and piecewise Lyapunov functions are used such that less conservative results can be obtained, moreover, gain performance improvement results are presented to show the advantage of reset control. Numerical examples are given to show the effectiveness.     

Passive Control for Stochastic Interval Systems with Interval Time‐Varying Delay

This paper is concerned with the problem of delay‐dependent passive analysis and control for stochastic interval systems with interval time‐varying delay. The system matrices are assumed to be uncertain within given intervals, and the time delay is a time‐varying continuous function belonging to a given range. By the transformation of the interval uncertainty into the norm‐bounded uncertainty, partitioning the delay into two segments of equal length, and constructing an appropriate Lyapunov–Krasovskii functional in each segment of the delay interval, delay‐dependent stochastic passive control criteria are proposed without ignoring any useful terms by considering the information of the lower bound and upper bound for the time delay. The main contribution of this paper is that a tighter upper bound of the stochastic differential of Lyapunov–Krasovskii functional is obtained via a newly‐proposed bounding condition. Based on the criteria obtained, a delay‐dependent passive controller is presented. The results are formulated in terms of linear matrix inequalities. Numerical examples are given to demonstrate the effectiveness of the method.     

Robust Stochastic Stability for a Class of Singular Systems with Uncertain Markovian Jump and Time‐Varying Delay

This paper deals with the problem of the robust stochastic stability for a class of singular systems with uncertain Markovian jump and time‐varying delay. Sufficient conditions on the stochastic stability are presented. The obtained results are formulated in terms of strict linear matrix inequalities. A numerical example is provided to show the effectiveness of the proposed approaches.     

Quantized Filtering for Continuous‐Time Markovian Jump Systems with Deficient Mode Information

This paper investigates the problem of quantized filtering for a class of continuous‐time Markovian jump linear systems with deficient mode information. The measurement output of the plant is quantized by a mode‐dependent logarithmic quantizer, and the deficient mode information in the Markov stochastic process simultaneously considers the exactly known, partially unknown, and uncertain transition rates. By fully exploiting the properties of transition rate matrices, together with the convexification of uncertain domains, a new sufficient condition for quantized performance analysis is first derived, and then two approaches, namely, the convex linearization approach and iterative approach, to the filter synthesis are developed. It is shown that both the full‐order and reduced‐order filters can be obtained by solving a set of linear matrix inequalities (LMIs) or bilinear matrix inequalities (BMIs). Finally, two illustrative examples are given to show the effectiveness and less conservatism of the proposed design methods.     

Robust observer‐based stabilization of Lipschitz nonlinear uncertain systems via LMIs ‐ discussions and new design procedure

This paper presents a new observer‐based controller design method for Lipschitz nonlinear systems with uncertain parameters and ‐bounded disturbance inputs. In the presence of uncertain parameters, the separation principle is not applicable even in the case of linear time invariant systems. A state of the art review for uncertain linear systems is first presented to describe the shortcomings and conservatism of existing results for this problem. Then a new LMI‐based design technique is developed to solve the problem for both linear and Lipschitz nonlinear systems. The features of the new technique are the use of a new matrix decomposition, the allowance of additional degrees of freedom in design of the observer and controller feedback gains, the elimination of any need to use equality constraints, the allowance of uncertainty in the input matrix and the encompassing of all previous results under one framework. An extensive portfolio of numerical case studies is presented to illustrate the superiority of the developed design technique to existing results for linear systems from literature and to illustrate application to Lipschitz nonlinear systems. Copyright © 2016 John Wiley & Sons, Ltd.     

On the Controllability of Nonlocal Second‐Order Impulsive Neutral Stochastic Integro‐Differential Equations with Infinite Delay

In this paper, we investigate the controllability for a class of nonlocal second‐order impulsive neutral stochastic integro‐differential equations with infinite delay in Hilbert spaces. More precisely, a set of sufficient conditions for the controllability results of nonlocal second‐order impulsive neutral stochastic integro‐differential equations with infinite delay are derived by means of the Banach fixed point theorem combined with theories of a strongly continuous cosine family of bounded linear operators. As an application, an example is provided to illustrate the obtained theory.     

State‐Feedback Stabilization of Stochastic Nonlinear Systems with Time‐Varying Delay and Different Orders

This paper studies the problem of state feedback stabilization for a class of stochastic time‐varying delay nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input. Based on the backstepping design method and the adding of a power integrator technique, a state feedback controller is constructed to ensure the origin of closed‐loop system is globally asymptotically stable in probability. The main design difficulty is how to deal with the different power orders, time‐varying delay and the nonsmooth system perturbations. The efficiency of the state feedback controller is demonstrated by a simulation example.     

On Near‐controllability of Discrete‐time Upper‐triangular Bilinear Systems with Applications to Controllability

Near‐controllability is defined for those systems that are uncontrollable but have a large controllable region. It is a property of nonlinear control systems introduced recently, and it has been demonstrated on two classes of discrete‐time bilinear systems. This paper studies near‐controllability of discrete‐time upper‐triangular bilinear systems, which are uncontrollable and are more general than the two classes mentioned. A necessary and sufficient condition for the systems in dimension two to be nearly controllable is presented, which covers the existing results. For the systems with high dimensions, necessary conditions and sufficient conditions of near‐controllability are provided, which generalize the existing results. In particular, the obtained near‐controllability results are applied to controllability of discrete‐time bilinear systems. An example also is given to demonstrate the effectiveness, which shows that the controllability problems of discrete‐time bilinear systems can be solved by near‐controllability.     

DISCRETIZING CONTINUOUS‐TIME CONTROLLERS WITH FUZZY LOGIC SYSTEMS AND ITS STABILITY ANALYSIS

In this paper, a new method, applying the fuzzy logic system, is proposed to discretize the continuous‐time controller in computer‐controlled systems. All the continuous‐time controllers can be reconstructed by the proposed method under the Sampling Theorem. That is, the fuzzy logic systems are used to add nonlinearity and to approximate smooth functions. Hence, the proposed controller is a new smooth controller that can replace the original controller, independent of the sampling time under the Sampling Theorem. Consequently, the proposed controller not only can discretize the continuous‐time controllers, but also can tolerate a wider range of sampling time uncertainty. Besides, the input‐output stability is proposed for discretizing the continuous‐time controller of the fuzzy logic systems. Finally, computer simulation shows that the proposed method can easily reconstructthe continuous‐time controller and has very good robustness for different sampling times.     

Ka‐band phased patch array antenna integrated with a PET‐controlled phase shifter

In this article, a 4 × 4 linear‐phased patch array antenna, consisting of four 1 × 4 patch subarrays and a true time‐delay multiline phase shifter, is proposed on a thin film liquid crystal polymer substrate at Ka‐band. The patch antenna is designed with a gain of 6 dBi at 35 GHz and a bandwidth of 23% centered at 35 GHz. To enhance the gain and symmetrize the beam patterns of the 4 × 4 array, a 1 × 4 patch subarray in the E‐plane was designed and characterized. The subarray produces an enhanced gain of 11 dBi and a wide beamwidth of ±38° in the H‐plane for beam steering. The proposed phase shifter comprises a 1 × 4 microstrip line power splitter and a piezoelectric transducer‐controlled phase perturber. A large phase variation of up to 370° and a low insertion loss of less than 2 dB were demonstrated for the phase shifter at Ka‐band. The integrated phased array attains a gain of 15.6 dBi, and a continuous true‐time delay beam steering of up to 33 ± 1° from 31 to 39 GHz. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:199–208, 2016.     

Adaptive Output Feedback Control for a Class of Uncertain Stochastic Nonlinear Systems With Unknown Time‐Delays

This paper investigates the problem of output feedback control for a class of stochastic nonlinear systems with time‐delays. Using dynamic gain scaling technique, an adaptive update law is introduced to the observer and controller to deal with the unknown parameters. Based on the Lyapunov‐Krasovskii functional and stochastic Barbalat's lemma, it is proved that the proposed universal‐type adaptive output feedback controller can regulate all the states of the closed‐loop system almost surely. A simulation example is presented to illustrate the effectiveness of the proposed design procedure.     

The Mixed Robust /FTS Control Problem Analysis and State Feedback Control

In this paper we deal with the mixed  /finite‐time stability control problem. More specifically, given an open loop uncertain linear system, we provide a necessary and sufficient condition for quadratic input‐output finite‐time stability with an  bound. Exploiting this result we also give a sufficient condition to solve the related synthesis problem via state‐feedback. The property of quadratic input‐output finite‐time stability with an  bound implies that the system under consideration satisfies an  performance bound between the disturbance input and the controlled output and, at the same time, is input‐output finite‐time stable for all admissible uncertainties. This condition requires the solution of a feasibility problem constrained by a pair of differential linear matrix inequalities (LMIs) coupled with a time‐varying LMI. The proposed technique is illustrated by means of both a numerical and a physical example.     

Optimal Control of Finite‐Valued Networks

Control of finite‐valued networks, including Boolean networks, is currently a hot topic. In this paper the optimization of the networks with time‐discounted performance criterion is discussed. The problem is formulated as a finite strategy game between human and machine. It is first proved that the optimal strategy can be found in the set of essentially periodic strategies, which makes the problem finitely computable, though the computational complexity of exhaustion might be a severe problem. Then an efficient numerical method is develossped to solve the problem. Some interesting examples are presented to demonstrate the efficiency of our results.