We address the secure control issue of networked non-affine nonlinear systems under denial of service (DoS) attacks. As for the situation that the system information cannot be measured in specific period due to the malicious DoS attacks, we design a neural networks (NNs) state observer with switching gain to estimate internal states in real time. Considering the error and dynamic performance of each subsystem, we introduce the recursive sliding mode dynamic surface method and a nonlinear gain function...

We consider a finite-dimensional control system $\left(\Sigma \right)\dot{x}\left(t\right)=f(x\left(t\right),u\left(t\right))$, such that there exists a feedback stabilizer $k$ that renders $\dot{x}=f(x,k\left(x\right))$ globally asymptotically stable. Moreover, for $(H,p,q)$ with $H$ an output map and $1\le p\le q\le \infty$, we assume that there exists a ${𝒦}_{\infty }$-function $\alpha$ such that $\parallel H\left(x_u\right){\parallel }_q\le {\alpha (\parallel u\parallel }_p)$, where $x_u$ is the maximal solution of ${\left(\Sigma \right)}_k\dot{x}\left(t\right)=f(x\left(t\right),k\left(x\left(t\right)\right)+u\left(t\right))$, corresponding to $u$ and to the initial condition $x\left(0\right)=0$. Then, the gain function $G_{(H,p,q)}$ of $(H,p,q)$ given by$$G_{(H,p,q)}\left(X\right)\stackrel{\mathrm{def}}{=}\underset{{\parallel u\parallel }_p=X}{sup}{\parallel H\left(x_u\right)\parallel }_q,$$is well-defined. We call profile of $k$ for $(H,p,q)$ any ${𝒦}_{\infty }$-function which is of the same order of magnitude as $G_{(H,p,q)}$. For the double integrator...

We consider a finite-dimensional control system $\left(\Sigma \right)\dot{x}\left(t\right)=f(x\left(t\right),u\left(t\right))$, such that there exists a feedback stabilizer k that renders $\dot{x}=f(x,k\left(x\right))$ globally asymptotically stable. Moreover, for (H,p,q) with H an output map and $1\le p\le q\le \infty$, we assume that there exists a ${𝒦}_{\infty }$-function α such that $\parallel H\left(x_u\right){\parallel }_q\le {\alpha (\parallel u\parallel }_p)$, where xu is the maximal solution of ${\left(\Sigma \right)}_k\dot{x}\left(t\right)=f(x\left(t\right),k\left(x\left(t\right)\right)+u\left(t\right))$, corresponding to u and to the initial condition x(0)=0. Then, the gain function $G_{(H,p,q)}$ of (H,p,q) given by 14.5cm $$G_{(H,p,q)}\left(X\right)\stackrel{\mathrm{def}}{=}\underset{{\parallel u\parallel }_p=X}{sup}{\parallel H\left(x_u\right)\parallel }_q,$$ is well-defined. We call profile of k for (H,p,q) any ${𝒦}_{\infty }$-function which is of the same order of...

The biped robot with flat feet and fixed ankles walking down a slope is a typical impulsive dynamic system. Steady passive gaits for such mechanism can be induced on certain shallow slopes without actuation. The steady gaits can be described by using stable non-smooth limit cycles in phase plane. In this paper, it is shown that the robot gaits are affected by three parameters, namely the ground slope, the length of the foot, and the mass ratio of the robot. As the ground slope is gradually increased,...

The polynomial matrix equation $X_l{D}_r$$+$$Y_l{N}_r$$=$$D_k$ is solved for those $X_l$ and $Y_l$ that give proper transfer functions $X_l^{-1}{Y}_l$ characterizing a subclass of compensators, contained in the class whose arbitrary element can be cascaded to a plant with the given strictly...

This note focuses on the study of robust H-sub-infinity control design for a kind of distributed parameter systems in which time-varying norm-bounded uncertainty enters the state and input operators. Through a fixed Lyapunov function, we present a state feedback control which stabilizes the plant and guarantees an H-sub-infinity norm bound on disturbance attenuation for all admissible uncertainties. In the process, we generalize some known results for finite dimensional linear systems.

The paper addresses receding-horizon (predictive) control for polytopic discrete-time systems subject to input/state constraints and unknown but bounded disturbances. The objective is to optimize nominal performance while guaranteeing robust stability and constraint satisfaction. The latter goal is achieved by exploiting robust invariant sets under linear and nonlinear control laws. Tradeoffs between maximizing the initial feasibility region and guaranteeing ultimate boundedness in the smallest...

This paper treats the question of robust control of chaos in modified FitzHugh-Nagumo neuron model under external electrical stimulation based on internal model principle. We first present the solution of the global robust output regulation problem for output feedback system with nonlinear exosystem. Then we show that the robust control problem for the modified FitzHugh-Nagumo neuron model can be formulated as the global robust output regulation problem and the solvability conditions for the output...

The paper addresses the problem of the robust output feedback controller design with a guaranteed cost and parameter dependent Lyapunov function for linear continuous time polytopic systems. Two design methods based on improved robust stability conditions are proposed. Numerical examples are given to illustrate the effectiveness of the proposed methods. The obtained results are compared with other three design procedures.