Joint state filtering and parameter estimation for linear stochastic time-delay systems

This paper presents the sliding mode mean-square and mean-module state filtering and parameter identification problems for linear stochastic systems with unknown parameters over linear observations, where unknown parameters are considered Wiener processes. The original problems are reduced to the sliding mode mean-square and mean-module filtering problems for an extended state vector that incorporates parameters as additional states. The obtained sliding mode filters for the extended state vector also serve as the optimal identifiers for the unknown parameters. Performance of the designed sliding mode mean-square and mean-module state filters and parameter identifiers are verified for both, stable and unstable, linear uncertain systems.

Cooperative output regulation problem for linear time-delay multi-agent systems under switching network

This paper deals with the problem of positive observation for linear time-delay systems for which the states take nonnegative values whenever the initial conditions are nonnegative. We focus on the design of positive observers (possibly with time-delay) which guarantee nonnegative estimates of the current states. We derive necessary and sufficient conditions for the existence of a positive observer (extended Luemberger-type) and show that the solvability of the problem can be decided via standard linear programming techniques. Moreover, on the negative side, it is shown that one cannot stabilize any unstable positive time-delay system by using extended Luenberger type positive observers. In other words, the separation principle does not hold.

This paper presents the mean-square joint state and diffusion coefficient (noise intensity) estimator for linear stochastic systems with unknown noise intensity over linear observations, where unknown parameters are considered Wiener processes. The original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states. Since the noise intensities cannot be observable in the original linear system, the new quadratic vector variable formed by the diagonal of the matrix square of the system state is introduced. The obtained mean-square filter for the extended state vector also serves as the optimal identifier for the unknown parameters. Performance of the designed mean-square state filter and parameter identifier is verified in an illustrative example.

Growing environmental concerns and shrinking water resources require methods beyond conventional wastewater treatment. Membrane bioreactor (MBR) is a technology that has become a ubiquitous choice for high quality treatment and reuse of wastewater. One of the key challenges in wastewater treatment is the high energy cost associated with aeration. MBR systems use feedback control to regulate the measured dissolved oxygen level at a predetermined set point by manipulating the blower throughputs. However, for high dynamic loads, feedback control may not result in the best performance and energy efficiency. Any attempt to optimize performance and power consumption beyond a simple controls strategy requires a proper trade‐off analysis between investments on additional sensors and the long‐term benefits. This article proposes a joint state and parameter estimation methodology, which measures and controls the MBR system using available measurements. Thus, limitations of feedback strategies can be overcome by predicting the impact of time varying disturbances on the outputs. The novelty in this approach is the ability to reconstruct the unknown states and parameters with available measurements. The unknown parameters are adaptively estimated online. Lyapunov's direct method is employed to show boundedness of state and parameter estimation errors. Simulation results illustrate the efficacy of the approach. Copyright © 2011 Curtin University of Technology and John Wiley & Sons, Ltd.

An iterative method for suboptimal control of linear time-delayed systems

Model-based prognostics approaches rely on physics-based models that describe the behavior of systems and their components. These models must account for the several different damage processes occurring simultaneously within a component. Each of these damage and wear processes contributes to the overall component degradation. We develop a model-based prognostics methodology that consists of a joint state-parameter estimation problem, in which the state of a system along with parameters describing the damage progression are estimated, followed by a prediction problem, in which the joint state-parameter estimate is propagated forward in time to predict end of life and remaining useful life. The state-parameter estimate is computed using a particle filter and is represented as a probability distribution, allowing the prediction of end of life and remaining useful life within a probabilistic framework that supports uncertainty management. We also develop a novel variance control algorithm that maintains an uncertainty bound around the unknown parameters to limit the amount of estimation uncertainty and, consequently, reduce prediction uncertainty. We construct a detailed physics-based model of a centrifugal pump that includes damage progression models, to which we apply our model-based prognostics algorithm. We illustrate the operation of the prognostic solution with a number of simulation-based experiments and demonstrate the performance of the approach when multiple damage mechanisms are active.

The confluence of nonlinearity, unavailable states, and unknown time-varying parameters poses profound estimation challenges in fractional-order dynamical systems. This paper presents a novel adaptive observer design for nonlinear fractional-order Lipschitz systems with unknown, slowly time-varying parameters. Drawing on recent advancements in fractional-order calculus, a rigorous stability analysis is conducted, deriving the updating law and formulating the observer’s viability and stability conditions in terms of linear matrix inequalities (LMIs) and linear matrix equalities (LMEs). The proposed observer ensures the stability of both state observation and parameter estimation errors, along with the asymptotic convergence of the observation error norm square mean value to zero. Empirical results from a case study on a fractional-order financial system validate the efficacy of the proposed observer, thereby advancing the field of states and parameters estimation theory for non-integer order nonlinear systems.

Reduced-order synchronization of time-delay chaotic systems with known and unknown parameters

Many stochastic optimal control problems have analytical solutions up to unknown numerical parameters. We demonstrate this fact with several examples from inventory theory, queuing theory, and risk theory. The paper reviews sufficient conditions for the existence of parametric optimal solutions to such problems in the stationary and nonstationary cases, for minimizing the average and discounted costs. The found parametric strategies are then substituted into the dynamic equations and the target functional of the primary optimal control problem. Thus, the original problem reduces to the problem of finite-dimensional stochastic programming concerning the unknown parameters. Since the optimal strategies are nonconvex, nonsmooth, or discontinuous functions of state variables and parameters, the corresponding stochastic programming problem may also be nonconvex, nonsmooth, or discontinuous. The paper proposes methods for calculating stochastic (quasi-)gradients (or their finite-difference analogs) of the objective function of the obtained stochastic programming problem and substantiates stochastic quasigradient methods for finding optimal parameter values. We illustrate the proposed solution approach by optimal inventory control and optimization of an energy accumulation system.

This paper considers the estimation problem for linear continuous-time systems with the interrupted observation mechanism which is characterized in terms of the jump Markov process taking on the values of 0 or 1. The minimum variance estimator algorithm is derived. The approach adopted here is that we express the jump process in terms of the initial value and the jump times instead of its instantaneous values and that in order to apply Lainiotis' formula we regard the initial value and jump times as the unknown system parameter vector. The parameter vector is, however, infinite dimensional so that Lainiotis' formula cannot be applied directly. This is because the formula is applicable only to linear systems with a finite dimensional parameter vector. Therefore, the minimum variance estimator algorithm is derived by using some limiting procedure. The resultant optimal algorithm is infinite dimensional, so that feasible approximate algorithms should be developed for practical implementation. A simple illustrating example is also worked out.

Based on complex scaling, the paper copes with stability analysis and stabilization of linear time-invariant continuous-time systems with multiple time delays in state, control input, and measured output, under state and/or output feedback. More specifically, the paper establishes stability criteria for exponential/asymptotical stability with Hurwitz complex scaling being applied to the related characteristic polynomials. The stability conditions are necessary and sufficient, delay-dependent, and independent of feedback structures and open-loop poles distribution. The criteria can be implemented graphically with locus plotting or numerically without it; moreover, no prior frequency sweeping is involved, and the contour and locus encirclement orientations can be self-defined. Exploiting the complex scaling approach and embracing its technical merits, it is considered to design static state feedback control for robustly stabilizing time-delayed systems. A small-gain interpretation for the suggested stabilization is also elaborated. Examples are included to illustrate the main results.

Network Control.- Delay-Based Non-linear Observers for Congestion Control in Communication Networks.- On the Use of State Predictors in Networked Control Systems.- Networked Control Systems: Algorithms and Experiments.- Modeling and Closed Loop Control for Resource-Constrained Load Balancing with Time Delays in Parallel Computations.- Stability of Load Balancing Control.- Teleoperation.- Robust H ? Control of Bilateral Teleoperation Systems Under Communication Time-Delay.- Web Remote Control of Mechanical Systems: Delay Problems and Experimental Measurements of Round Trip Time.- PDE Approach for Time Delays in Robotized Teleoperation.- Emerging Methodologies.- From Time Delay to Distributed Parameter Systems in Communications.- Computing Maximum Delay Deviation Allowed to Retain Stability in Systems with Two Delays.- On Exact Controllability of Linear Time Delay Systems of Neutral Type.- New Computational Methods.- Applied Interval Computation: A New Approach for Time-Delays Systems Analysis.- Mathematical and Computational Tools for the Stability Analysis of Time-Varying Delay Systems and Applications in Mechanical Engineering.- Diffusive Representation for Operators Involving Delays.- OreModules: A Symbolic Package for the Study of Multidimensional Linear Systems.- Predictors, Inversion and Filtering.- Inversion and Tracking Problems for Time Delay Linear Systems.- Finite Impulse Response Systems for Almost Perfect Decoupling in Nonminimum-Phase Plants.- Linearization of the Power Amplifier in Mobile Telecommunications.- Merging Saturations and Input Delays.- Robust Sampled-Data Control: An Input Delay Approach.- Stabilization and Finite-Gain Stabilizability of Delay Linear Systems Subject to Input Saturation.- Global Asymptotic Stabilization of a PVTOL Aircraft Model with Delay in the Input.

H ∞ full information control method for structural vibration suppression with control delay is proposed within a discrete-time framework. Firstly, the continuous-time system equation with control delay is discretized by precise computation of matrix exponentials. By introducing an appropriate extended state vector, the time-delay system is transformed into standard discrete forms without time delays. Then a controller is designed based on the discrete time H ∞ full information control theory. The controller consists of a regular feedback closed-loop and a feed-forward compensator which utilizes external excitation signals measured in real time. The feed-forward plus feedback controller has better performance than feedback only controllers. The feedback loop of the deduced controller contains linear combinations of former control inputs besides the current state feedback terms. Thus the proposed method is applicable to large time-delay cases. Considering the complexity of the transformed system, a 2 N algorithm is introduced to search the optimal attenuation level and evaluate the control law. The present algorithm can be executed parallel, which makes the design of H ∞ controllers very convenient. Finally, numerical simulations of a three-story structure control are implemented. Time-delay effects on the optimal attenuation level are given to show that it is an important factor for system stability. Simulation results demonstrate the feasibility and effectiveness of the proposed control method.

Studies the optimal guaranteed control problem for a class of linear uncertain time-delay systems. The systems under consideration are described by state differential equations with time-varying unknown but norm-bounded uncertain parameters and time-varying unknown but bounded delay in states. An upper bound of the performance measured by standard quadratic function is constructed and based on the delay-dependent stabilizing approach, a method of designing a state feedback robust quadratic stabilizing control law guaranteeing this quadratic performance index be less than the constructed upper bound is derived. A procedure is given to select an optimal state feedback controller in the sense of minimizing this upper bound of the quadratic performance index. The results depend on the size of delay and are given in terms of several linear matrix inequalities.