Semiglobal Robust Stabilization of Nonlinear Systems without Vanishing Condition

The authors provide an alternative solution to the problem of semiglobal stabilization of a class of minimum phase nonlinear systems that was considered by A.R. Teel (1991). The method used yields a stabilizing linear state feedback law in contrast to a nonlinear state feedback law proposed by Teel. The peaking phenomenon is eliminated by inducing a specific time-scale structure in the linear part of the closed-loop system. This structure consists of a very slow and a very fast time scale. The crucial component in the method is the relation between the slow and the fast time-scales. The proposed linear state feedback control law has a single tunable gain parameter that allows for local asymptotic stability and regulation to the origin for any initial condition in some a priori given (arbitrarily large) bounded set. >

Stability Analysis and Control of Bilinear Discrete-Time Systems: A Dual Approach

Memoryless H∞ controller for singular systems with delayed state and control

The robust H∞ control problem for time-varying uncertain linear systems with time-varying state, and control delays is considered. Based on the Riccati equation approach, we design a robust H∞ linear time-invariant state feedback control law, which stabilizes the system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. A sufficient condition for the existence of the. robust H∞ controller is derived and two synthesis methods are presented for a robust H∞ control law to uncertain time-delay systems. One is to construct a robust H∞ control law by an equivalent linear time-invariant structural description for the sufficient condition and the control law can be obtained by solving an algebraic Riccati equation (ARE). The other method is to transform the sufficient condition into a linear matrix inequality (LMF) problem and the control law can be obtained by solving the LMI. A numerical example is presented to illustrate the obtained results.

Decentralized Output Feedback Control of Interconnected Uncertain Delay Systems

Global Mittag–Leffler stabilization of fractional-order bidirectional associative memory neural networks

We provide an alternative solution to the problem of semi‐global stabilization of a class of minimum phase nonlinear systems which is considered in Reference 17. Our method yields a stabilizinglinearstate feedback law in contrast to anonlinearstate feedback law proposed in Reference 17. We eliminate the peaking phenomenon by inducing a specific time‐scale structure in the linear part of the closed‐loop system. This time‐scale structure consists of a very slow and a very fast time scale. The crucial component in our method is the relation between the slow and the fast time scales. Our proposed linear state feedback control law has asingletunable gain parameter that allows for local asymptotic stability and regulation to the origin for any initial condition in somea priorigiven (arbitrarily large) bounded set.

The existence, uniqueness, and stability of equilibrium points in nonlinear systems are often challenged by parameter variations, which can limit the effectiveness of conventional stability analysis methods. This paper addresses the parametric quadratic stabilization of discrete-time uncertain nonlinear systems with parameter-dependent coefficients and sector-bounded nonlinearities. A linear state feedback control law is designed, and a parameter-dependent linear matrix inequality (LMI) condition is derived to guarantee the existence, uniqueness, and quadratic stability of a closed-loop equilibrium point. To handle parameter uncertainties, a sequential randomized algorithm is applied, yielding a probabilistic solution that ensures parametric quadratic stabilization with high confidence.

A new robust model predictive control (MPC) approach is proposed for constrained linear systems in this paper. It adopts a contractive state set as terminal set in MPC problem and employs a novel function of the state with respect to this terminal set as the stage cost of the objective function. When the controlled systems are subject to linear constraints, explicit MPC law can be obtained as a piecewise affine linear state feedback control law via multi-parameter linear programming method. The presented MPC, along with linear variable-structure control law associated with the terminal set, is essentially a dual mode control scheme to stabilize the constrained uncertain linear system. Compared to the existing MPC methods, the proposed approach have both better real-time applicability and more general robust stability guarantee.

On interval observer design for active Fault Tolerant Control of Linear Parameter-Varying systems

This paper presents a novel integral sliding mode control (ISMC) for singularly perturbed systems (SPSs) with matched disturbances. Firstly, a linear state feedback control law for the fast subsystem of SPS is designed, and the slow subsystem can be obtained. Secondly, an ISMC incorporating the disturbance estimate provided by a disturbance observer is designed. In order to attenuate matched disturbances, the Lyapunov function is employed to determine the gain of ISMC by solving a linear matrix inequality (LMI). As a result, the closed-loop slow subsystem under the ISMC is exponentially stable, and the full-order SPSs are exponentially stable under the composite control law. Finally, the effectiveness and advantages of the proposed method are demonstrated by simulations.

This paper is dealing with the receding horizon optimal control techniques having as main goal the reduction of the computational effort inherent to the use of on-line optimization routines. The off-line construction of the explicit solution for the associated multiparametric optimization problems is advocated with a special interest in the presence of nonlinearities in the constraints description. The proposed approach is a geometrical one, based on the topology of the feasible domain. The resulting piecewise linear state feedback control law has to accept a certain degree of suboptimality, as it is the case for local linearizations or decompositions over families of parametric functions. In the presented techniques, this is directly related to the distribution of the extreme points on the frontier of the feasible domain.

The application of a metaheuristic search algorithm is proposed to determine the degrees of freedom of a linear state feedback control law, designed to achieve independent force and position control of multitask cooperating robotic manipulators. The determination of the appropriate values for the controller's degrees of freedom may be formulated as an optimization under constraints problem. The metaheuristic search algorithm provides an easy to implement and computationally efficient solution for this problem, which is complicated due to the large number of constraints, in addition to the highly nonlinear structure of the functions that determine the squeezing forces.

In this paper, we develop an adaptive inverse compensation scheme for controlling the aerodynamic flow of a synthetic jet actuator on a dynamic aircraft system. An adaptive inverse is employed for cancelling the effect of the nonlinearity of the synthetic jet. A linear state feedback control law is used for controlling the aircraft dynamics. A linearly parametrized error model is derived for the nonlinear actuator model. A parameter projection adaptive law is used to ensure desired closed-loop stability and asymptotic tracking. An application of this adaptive compensation scheme to the control of a linear aircraft model with a synthetic jet actuator is studied and its effectiveness is verified by simulation results.

EXPLICIT HYBRID OPTIMAL CONTROLLER FOR DISTURBANCE ATTENUATION IN LINEAR HYBRID SYSTEMS