Michael V. Basin

Reliable Filtering With Strict Dissipativity for T-S Fuzzy Time-Delay Systems

In this paper, the problem of reliable filter design with strict dissipativity has been investigated for a class of discrete-time T-S fuzzy time-delay systems. Our attention is focused on the design of a reliable filter to ensure a strictly dissipative performance for the filtering error system. Based on the reciprocally convex approach, firstly, a sufficient condition of reliable dissipativity analysis is proposed for T-S fuzzy systems with time-varying delays and sensor failures. Then, a reliable filter with strict dissipativity is designed by solving a convex optimization problem, which can be efficiently solved by standard numerical algorithms. Finally, numerical examples are provided to illustrate the effectiveness of the developed techniques.

Predictive Output Feedback Control for Networked Control Systems

This paper studies the problem of predictive output feedback control for networked control systems (NCSs) with random communication delays. A networked-predictive-control scheme is employed to compensate for the network-induced delay. Furthermore, the time-varying predictive controller with mixed random delays for networked systems is introduced. Then, the system is formulated as a Markovian jump system. New techniques are presented to deal with the distributed delay in the discrete-time domain. Based on the analysis of closed-loop NCSs, the designed predictive time-varying output feedback controller can guarantee system stability. Simulation example demonstrates the compensation for random communication delays and data loss in networked systems using the proposed predictive scheme.

Two-Dimensional Dissipative Control and Filtering for Roesser Model

This paper investigates the problems of two-dimensional (2-D) dissipative control and filtering for a linear discrete-time Roesser model. First, a novel sufficient condition is proposed such that the discrete-time Roesser system is asymptotically stable and 2-D (Q, S, R)-α-dissipative. Special cases, such as 2-D passivity performance and 2-D H∞ performance, and feedback interconnected systems are also discussed. Based on this condition, new 2-D (Q, S, R)-α-dissipative state-feedback and output-feedback control problems are defined and solved for a discrete-time Roesser model. The design problems of 2-D (Q, S, R)-α-dissipative filters of observer form and general form are also considered using a linear matrix inequality (LMI) approach. Two examples are given to illustrate the effectiveness and potential of the proposed design techniques.

Quantized Control Design for Cognitive Radio Networks Modeled as Nonlinear Semi-Markovian Jump Systems

This paper is concerned with the quantized control design problem for a class of semi-Markovian jump systems with repeated scalar nonlinearities. A semi-Markovian system of this kind has been transformed into an associated Markovian system via a supplementary variable technique and a plant transformation. A sufficient condition for associated Markovian jump systems is developed. This condition guarantees that the corresponding closed-loop systems are stochastically stable and have a prescribed H∞ performance. The existence conditions for full- and reduced-order dynamic output feedback controllers are proposed, and the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one, which can be solved efficiently with existing optimization techniques. Finally, an application to cognitive-radio systems demonstrates the efficiency of the new design method developed.

Optimal control for linear systems with multiple time delays in control input

This note presents the optimal linear-quadratic (LQ) regulator for a linear system with multiple time delays in the control input. Optimality of the solution is proved in two steps. First, a necessary optimality condition is derived from the maximum principle. Then, the sufficiency of this condition is established by verifying that it satisfies the Hamilton-Jacobi-Bellman equation. Using an illustrative example, the performance of the obtained optimal regulator is compared against the performance of the optimal LQ regulator for linear systems without delays and some other feasible feedback regulators that are linear in the state variables. Finally, the note establishes a duality between the solutions of the optimal filtering problem for linear systems with multiple time delays in the observations and the optimal LQ control problem for linear systems with multiple time delays in the control input.

Sliding mode attitude tracking of rigid spacecraft with disturbances

Abstract The attitude tracking control problem of a spacecraft nonlinear model with external disturbances and inertia uncertainties is addressed in this paper. First, a new sliding mode controller is designed to ensure the asymptotic convergence of the attitude and angular velocity tracking errors against external disturbances and inertia uncertainties by using a modified differentiator to estimate the total disturbances. Second, an adaptive algorithm is applied to compensating the disturbances, by which another sliding mode controller is successfully designed to achieve a high performance on the attitude tracking in the presence of the inertia uncertainties, external disturbances and actuator saturations. Finally, simulation results are presented to illustrate effectiveness of the control strategies.

Itô–Volterra Optimal State Estimation With Continuous, Multirate, Randomly Sampled, and Delayed Measurements

The optimal filter for continuous, linear, stochastic, time-varying systems described by the Itocirc-Volterra equations with discontinuous measure is derived. With an appropriately selected measure, the result is applicable to a wide range of observation processes, including the hybrid case of observations formed by an arbitrary combination of continuous and discrete measurements, which may be sampled with a priori unknown, changing, and, possibly, random rates and delays. The simultaneous presence of continuous and sampled measurements causes impulsive discontinuity in the inputs of the optimal filter equations, which leads to a discontinuous change in state estimates every time a sampled measurement becomes available. Using the theory of vibrosolutions, the explicit and unique expressions for the jumps in state estimates and estimation error covariance are derived. Several examples illustrate the procedure of modeling hybrid measurement systems by selecting an appropriate discontinuous measure. We further show that the Itocirc-Volterra model and the main result of the paper can be specialized to several important cases, including state space systems, for which we recover several known state estimation results, and derive a novel optimal filter for continuous LTV systems with an arbitrary combination of continuous and delayed sampled measurements. This optimal filter updates the state estimates for incoming measurements as soon as they become available and does not require prior knowledge of sampling instants and delays, which makes it applicable when deterministic and random changes in sampling and delays are present. Several computational examples demonstrate the implementation of the developed filter and compare its performance to the traditional alternatives using Monte-Carlo simulations

Deadbeat Dissipative FIR Filtering

In this paper, we propose a new deadbeat dissipative filter with a finite impulse response (FIR) structure for linear discrete-time systems with external disturbance; this filter is called a deadbeat dissipative FIR filter (DDFF). The new filter ensures (Q, S, R)-α-dissipativity and the deadbeat property based on three slack matrix variables. By tuning the weighting parameters provided by the (Q, S, R)-α-dissipativity in the proposed DDFF, we present H∞ and passive FIR filters in a unified framework and investigate ways of improving the ℓ2 stability, bounded- disturbance bounded-error stability, and robustness of FIR filters. The gain matrix of the proposed DDFF is obtained by solving a convex problem using the linear matrix inequality approach. Two numerical examples are provided to demonstrate the effectiveness and advantages of the obtained theoretical results.

Central suboptimal H ∞ filter design for linear time-varying systems with state and measurement delays

This article presents the central finite-dimensional H ∞ filters for linear systems with state and measurement delay that are suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the results previously obtained for linear time delay systems, this article reduces the original H ∞ filtering problem to H 2 (optimal mean-square) filtering problem using the technique proposed in Doyle, Glover, Khargonekar, and Francis (1989 ‘State-space Solutions to Standard H 2 and H ∞ Control Problems’, IEEE Transactions on Automatic Control, 34, 831–847). Application of the reduction technique becomes possible, since the optimal closed-form filtering equations solving the H 2 (mean-square) filtering problem have been obtained for linear systems with state and measurement delays. This article first presents the central suboptimal H ∞ filter for linear systems with state and measurement delays, based on the optimal H 2 filter from Basin, Alcorta-Garcia, and Rodriguez-Gonzalez (2005, ‘Optimal Filtering for Linear Systems with State and Observation Delays’, International Journal of Robust and Nonlinear Control, 15, 859–871), which consists, in the general case, of an infinite set of differential equations. Then, the finite-dimensional central suboptimal H ∞ filter is designed in case of linear systems with commensurable state and measurement delays, which contains a finite number of equations for any fixed filtering horizon; however, this number still grows unboundedly as time goes to infinity. To overcome that difficulty, the alternative central suboptimal H ∞ filter is designed for linear systems with state and measurement delays, which is based on the alternative optimal H 2 filter from Basin, Perez, and Martinez-Zuniga (2006, ‘Alternative Optimal Filter for Linear State Delay Systmes’, International Journal of Adaptive Control and Signal Processing, 20, 509–517). In all cases, the standard H ∞ filtering conditions of stabilisability, detectability and noise orthonormality are assumed. Finally, to relax the standard conditions, this article presents the generalised versions of the designed H ∞ filters in the absence of the noise orthonormality. The proposed H ∞ filtering algorithms provide direct methods to calculate the minimum achievable values of the threshold γ, based on the existence properties for a bounded solution of the gain matrix equation. Numerical simulations are conducted to verify the performance of the designed central suboptimal filters for linear systems with state and measurement delays against the central suboptimal H ∞ filter available for linear systems without delays. The simulation results show a definite advantage in the values of the noise-output transfer function H ∞ norms in favour of the designed filters.

Optimal and robust control for linear state-delay systems

This paper presents the optimal regulator for a linear system with state delay and a quadratic criterion. The optimal regulator equations are obtained using the maximum principle. Performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulator available for linear systems without delays. Simulation graphs demonstrating better performance of the obtained optimal regulator are included. The paper then presents a robustification algorithm for the obtained optimal regulator based on integral sliding mode compensation of disturbances. The general principles of the integral sliding mode compensator design are modified to yield the basic control algorithm oriented to time-delay systems, which is then applied to robustify the optimal regulator. As a result, the sliding mode compensating control leading to suppression of the disturbances from the initial time moment is designed. The obtained robust control algorithm is verified by simulations in the illustrative example.