H2−H∞ control of discrete-time nonlinear systems using the state-dependent Riccati equation approach

Controllability Issues in Nonlinear State-Dependent Riccati Equation Control

In the last few years, algorithms using state-dependent Riccati equations (SDREs) have been proposed for solving nonlinear control problems. Under state feedback, pointwise solutions of an SDRE must be obtained along the system trajectory. To ensure the control is well-defined, global controllability and observability of state-dependent system factorizations are commonly assumed. This paper rig...

State Dependent Differential Riccati Equation for Nonlinear Estimation and Control

State-dependent Riccati equation (SDRE) methods for designing control algorithms and observers for nonlinear processes entail the use of algebraic Riccati equations. These methods have yielded a number of impressive results, however, they can be computationally quite intensive and thus far they have not yielded to those attempting to assess their stability. This paper explores an alternative, t...

Solutions of the Riccati equation for H Discrete Time Systems

Let H and Y be separable Hilbert spaces, and U finite dimensional. Let A ∈ L(H), B ∈ L(U,H), C ∈ L(H,Y ), D ∈ L(U, Y ), and suppose that the open loop transfer function D(z) := D+zC(I−zA)B ∈ H(D;L(U, Y )), where D is the open unit disk. We consider a subset of self adjoint solutions P of the discrete time algebraic operator Riccati equation (DARE)    APA− P + CJC = K PΛPKP , ΛP = D JD +BPB...

The discrete Riccati equation of optimal control

Optimal Finite-time Control of Positive Linear Discrete-time Systems

This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity proper...