Abstract: A new adaptive fuzzy fault-tolerant control scheme for complex non-linear systems is proposed in this paper. The approach presented here combines fuzzy T-S dynamic model with Riccati equation. In each local linear model of the fuzzy dynamic model, Riccati equation is used in the design of fault-tolerant control. These local models are linked together by fuzzy membership functions to f...

It is shown that, under appropriate assumptions, the continuous algebraic Riccati equation with Toeplitz matrices as coefficients has Toeplitz-like solutions. Both infinite and sequences of finite Toeplitz matrices are considered, and also studied is the finite section method, which consists in approximating infinite systems by large finite truncations. The results are proved by translating the...

Here ordinary differential equations of third and higher order are considered; in particular, a class of equations which can be solved by quadratures is exploited. Indeed, crucial to obtain our result is the property of the Riccati equation, according to which, given one particular solution, then its general solution can be determined explicitly. Thus, what we term the “Riccati” Property is int...

In this paper we propose a nonrecursive method for solving the general discrete-time algebraic Riccati equation related to the Hm control problem (Hm-DARE). We have achieved this by casting the problem of solving a given H,-DARE to the problem of solving an auxiliary continuous-time algebraic Riccati equation associated with the H , control problem (Hm-CARE) for which the well known nonrecursiv...

Abstract. We study an algorithm for the numerical solution of algebraic matrix Riccati equations that arise in linear optimal control problems. The algorithm can be considered to be a multishift technique, which uses only orthogonal symplectic similarity transformations to compute a Lagrangian invariant subspace of the associated Hamiltonian matrix. We describe the details of this method and co...

In this paper we give a nonoscillation criterion for half-linear equations with periodic coefficients under fixed moments of impulse actions. The method is based on existence of positive solutions of the related Riccati equation and a recently obtained comparison principle. In the special case when the equation becomes impulsive Hill equation new oscillation criteria are also obtained.

This paper concerns second order sufficient conditions of optimality, involving the Riccati equation, for optimal control problems with periodic boundary conditions. The problems considered involve no pathwise constraints and are ‘regular’, in the sense that the strengthened Legendre-Clebsch condition is assumed to be satisfied. A well-known sufficient condition, which we refer to as the Riccat...

We study the (3+1)-dimensional stochastic Jimbo–Miwa (SJM) equation induced by multiplicative white noise in Itô sense. employ Riccati mapping and He’s semi-inverse techniques to provide trigonometric, hyperbolic, rational function solutions of SJME. Due applications ocean studies other disciplines, acquired may explain numerous fascinating physical phenomena. Using a variety 2D 3D diagrams, we...

Both linear time-invariant (LTI) and linear time-varying (LTV) systems are addressed. They are placed in a unified conceptual framework. The characteristic equation for each subclass is formulated as a Riccati equation. Where LTI-systems lead to algebraic Riccati equations, the LTV-case generalizes this result to differential Riccati equations.

This paper is concerned with a general non-homogeneous stochastic linear quadratic (LQ) control problem regime switching and random coefficients. We obtain the explicit optimal state feedback value for this in terms of two systems backward differential equations (BSDEs): one famous Riccati equation other new multi-dimensional BSDE all coefficients being unbounded. The existence uniqueness solut...