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This paper is concerned with the sliding mode control (SMC) via finite-time stabilization (FTS) for a class of conic-type nonlinear semi-Markovian jumping systems (SMJSs). Comparing with the classical Markovian jumping systems, the transition rates of SMJSs are related to the random sojourn-time $g$. Based on this, a suitable SMC law for driving the state trajectories to the designed sliding surface within a finite-time interval is given. Then, the FTS over reaching phase and sliding motion phase is further proved to guarantee the FTS of the whole SMJSs. Finally, the effectiveness of the proposed method is demonstrated by a time-delayed Chua’s circuit simulation. [ABSTRACT FROM AUTHOR]

This paper studies the $ {H}_{ {\infty }}$ sliding mode control (SMC) problem for a class of discrete-time conic-type nonlinear systems with time-delays and uncertainties. The nonlinear terms satisfy the conic-type constraint condition that lies in a know hyper-sphere with an uncertain center. By choosing a proper Lyapunov candidate, sufficient conditions are derived to ensure the asymptotic stability of the sliding mode dynamics while achieving a prescribed $ {H}_{ {\infty }}$ disturbance attenuation level and finally converted into a minimization problem. The controller is constructed to guarantee the discrete-time reach condition and maintain the states on the prespecified sliding surface. A simulation result and a practical example related to the Chua’s circuit are given at last to show the validity of our SMC strategy. [ABSTRACT FROM AUTHOR]

This paper investigates the asynchronous resilient controller design problem for a class of nonlinear switched systems with time-delays and uncertainties in a given finite-time interval. By constructing proper multiple Lyapunov–Krasovskii functions and applying average dwell time methods, a switching law and the relevant asynchronous resilient controller are designed to guarantee the finite-time boundedness of the closed-loop system with a specified ${H} _{\infty }$ performance index. The ${H} _{\infty }$ resilient controller design problems can be derived by solving a set of linear matrix inequalities. A practical example is employed to demonstrate the availability of the proposed methods. [ABSTRACT FROM AUTHOR]

The finite-time sliding mode controller design problem of a class of conic-type nonlinear systems with time-delays and mismatched external disturbance is studied. The time-delay conic nonlinearities are considered to lie in a known hypersphere with an uncertain center. A scalar selection criterion dependent sliding mode control (SMC) law is constructed to drive the state trajectories onto the specified sliding surface during any assigned short time interval. By using slack matrix approach, a delay-dependent sufficient condition is derived to ensure the finite-time boundedness of the closed-loop systems over the finite-time interval. Then, the algorithm for designing the finite-time SMC law is established. Finally, two examples related to the time-delayed Chua’s circuit is given to demonstrate the effectiveness of the developed methods. [ABSTRACT FROM AUTHOR]

The finite-time passive control for a class of nonlinear uncertain systems with time-delays and uncertainties is studied. The nonlinear parameters are satisfied Lipschitz conditions. An optimal robust passive controller with respect to the finite-time interval is designed while the exogenous disturbances are unknown but energy bounded. Based on passive control theory, the sufficient condition for the existence of finite-time robust passive controller is given. This condition such that the resulting closed-loop system is finite-time boundedness (FTB) for all admissible uncertainties and satisfies the given passive control index. By using the constructed Lyapunov function, and applying linear matrix inequalities techniques (LMIs), the design method of the finite-time optimal passive controller is derived and can be obtained. Simulation results demonstrate the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

The observer-based finite-time passive control problem of a class of Lipschitz nonlinear systems with uncertainties and time delays is studied. The nonlinear parameters are considered to satisfy the global Lipschitz conditions and the exogenous disturbances are unknown but energy-bounded. By constructing an appropriate Lyapunov function, a observer-based state feedback controller is designed to guarantee that the resulting closed-loop system is finite-time bounded and satisfies the given passive constraint condition. Some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities. Simulation results illustrate the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the robust fault detection filter (RFDF) design problems for uncertain nonlinear Markov jump systems with state delays and parameter uncertainties. By means of Takagi–Sugeno fuzzy models, the dynamics of filtering error generator and the fuzzy RFDF system are constructed. With the aid of the selected weighting matrix function, the design objective is to find an optimal RFDF which results in a minimal difference between the reference model (ideal solution) and the RFDF (real solution) to be designed. A sufficient condition is firstly established on the stochastic stability by using stochastic Lyapunov–Krasovskii functional approach. Then in terms of linear matrix inequalities techniques, sufficient conditions on the existence of fuzzy RFDF are presented and proved. Finally, the design problem is formulated as an optimization algorithm. Simulation results illustrate that the proposed RFDF can detect the faults shortly after the occurrences. [Copyright &y& Elsevier]

• Fault detection scheme for conic nonlinear systems in finite frequency domain is designed. • Sufficient conditions to realize H_ fault sensitivity and H_ disturbance attenuation. • The fuzzy fault detection problem is transformed into an optimization algorithm. • A tunnel diode-circuit is given to confirm the validity of the designed scheme. In this paper, we focused on the issue of fault detection subject to a class of conic-type nonlinear systems in the finite frequency domain (FFD). Applying Takagi Sugeno (T-S) fuzzy models, the conic-type dynamic error system is established. To prove that the residual vector is robust to external disturbances and sensitive to faults, we provide some conditions to realize H − fault sensitivity performance and H ∞ disturbance attenuation performance within the FFD. Then, utilizing linear matrix inequalities techniques, the fuzzy fault detection observer design problem is transformed into an optimization algorithm. Finally, a numerical example related to a tunnel diode-circuit is given to confirm the validity of the designed scheme. [ABSTRACT FROM AUTHOR]

In this paper, a new online adaptive optimal controller design scheme is studied for a class of nonlinear systems with input time-delays. First, we linearize the original nonlinear systems by means of linear differential inclusion technique. Then the adaptive optimal controller of the linearized systems with input time-delays is obtained by online policy iteration algorithm. It also proves the convergence of the designed adaptive optimal control algorithm. Finally, the effectiveness of the proposed method is verified by two simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, a novel scheme for the tracking problem of nonlinear systems is proposed. First, as a new technology of neural network in control field, linear differential inclusion is used to approximate the nonlinear term for the entire system. Based on the equivalent linear system, tracking reference signal is given and a new augmented system is built. According to the mentioned value function, two reinforcement learning algorithms are proposed to design the optimal control law. Notice that the online algorithm does not involve the system dynamics and tracking dynamics. In the simulation section, the model of trolley system is given to prove the effectiveness and accuracy of the scheme proposed in this paper. [ABSTRACT FROM AUTHOR]