Michael A. Demetriou

Model Reference Adaptive Control of Distributed Parameter Systems

A model reference adaptive control law is defined for nonlinear distributed parameter systems. The reference model is assumed to be governed by a strongly coercive linear operator defined with respect to a Gelfand triple of reflexive Banach and Hilbert spaces. The resulting nonlinear closed-loop system is shown to be well posed. The tracking error is shown to converge to zero, and regularity results for the control input and the output are established. With an additional richness, or persistence of excitation assumption, the parameter error is shown to converge to zero as well. A finite-dimensional approximation theory is developed. Examples involving both first- and second-order, parabolic and hyperbolic, and linear and nonlinear systems are discussed, and numerical simulation results are presented.

Guidance of Mobile Actuator-Plus-Sensor Networks for Improved Control and Estimation of Distributed Parameter Systems

This paper presents an abstract framework for the optimization of actuating and sensing devices in distributed parameter systems. The optimization is performed on the repositioning of these devices throughout the spatial domain. It is assumed that a network of mobile sensing and actuating devices is available to obtain measurements from the spatially distributed process and dispense control signals to the spatially distributed process. By taking advantage of the properties that the spatial operator that governs the process dynamics possesses, namely symmetry, coercivity and boundedness, a scheme for the guidance of a mobile actuator-plus-sensor network is developed and used for the performance enhancement of the spatial process. The class of systems is governed by diffusion PDEs equipped with actuators having a boxcar spatial distribution and a collocated sensing device that provides the spatially averaged state measurement over the range of the actuating device. Using Lyapunov stability arguments, a stable guidance scheme is provided for each of the mobile agents. Due to the specific structure of the closed loop system operator with time-varying input and output operators, the same guidance schemes are applicable to the dual problem of mobile sensors employed for enhancing the state estimation problem. Both a centralized state estimator with mobile sensors and a network of consensus distributed estimators are considered, since both filters can be shown to result in the specific algebraic structure of a symmetric spatial operator with collocated input and output operators. Extensive numerical simulations for a 1-D diffusion equation with two actuator/sensor agents, a 2-D diffusion equation with one collocated actuator/sensor agent plus a centralized filter for a 1-D diffusion equation are included to verify the effectiveness of a such a mobile actuator-plus-sensor network in suppressing the effects of spatially varying disturbances and enhancing the systems performance.

Design of consensus and adaptive consensus filters for distributed parameter systems

This work establishes an abstract framework that considers the distributed filtering of spatially varying processes using a sensor network. It is assumed that the sensor network consists of groups of sensors, each of which provides a number of state measurements from sensing devices that are not necessarily identical and which only transmit their information to their own sensor group. A modification to the local spatially distributed filters provides the non-adaptive case of spatially distributed consensus filters which penalize the disagreement amongst themselves in a dynamic manner. A subsequent modification to this scheme incorporates the adaptation of the consensus gains in the disagreement terms of all local filters. Both the well-posedness of these two consensus spatially distributed filters and the convergence of the associated observation errors to zero in appropriate norms are presented. Their performance is demonstrated on three different examples of a diffusion partial differential equation with point measurements.

On-Line Parameter Estimation for Infinite-Dimensional Dynamical Systems

The on-line or adaptive identification of parameters in abstract linear and nonlinear infinite-dimensional dynamical systems is considered. An estimator in the form of an infinite-dimensional linear evolution system having the state and parameter estimates as its states is defined. Convergence of the state estimator is established via a Lyapunov estimate. The finite-dimensional notion of a plant being sufficiently rich or persistently excited is extended to infinite dimensions. Convergence of the parameter estimates is established under the additional assumption that the plant is persistently excited. A finite-dimensional approximation theory is developed, and convergence results are established. Numerical results for examples involving the estimation of both constant and functional parameters in one-dimensional linear and nonlinear heat or diffusion equations and the estimation of stiffness and damping parameters in a one-dimensional wave equation with Kelvin--Voigt viscoelastic damping are presented.

Adaptive reorganization of switched systems with faulty actuators

The objective of the note is to introduce an intelligent controller reorganization for systems with actuator failures (outages). An adaptive detection observer is utilized to monitor the system for possible actuator outages and a control logic is incorporated to switch (reorganize) the control policy the instant an actuator failure is detected in order to improve performance. The system under consideration is assumed to be square and the requisite control and stability arguments for failure detection and accommodation are similar to those for switched systems and which employ LMIs for controller design.

Optimal actuator/sensor location for active noise regulator and tracking control problems

In this paper, we investigate the problem of finding the optimal location of sensors and actuators to achieve reduction of the noise field in an acoustic cavity. We offer two control strategies: the first is based on linear quadratic tracking where the offending noise is tracked, and the second considers the formulation of the harmonic control strategy as a periodic static output feedback control problem. The first method, which is based on full state information, is suitable for optimal location of actuators while the second strategy can extend the results to finding optimal location of sensors as well as actuators. For both methods we consider the optimization of an appropriate quadratic performance criterion with respect to the location of the actuators and/or the sensors. Numerical examples are presented to compare the effectiveness of each control strategy and also the effect of optimal placement of actuators and sensors.

Natural second-order observers for second-order distributed parameter systems

The aim of this manuscript is to present an alternative method for designing state observers for second-order distributed parameter systems without resorting to a first-order formulation. This method has the advantage of utilizing the algebraic structure that second-order systems enjoy with the obvious computational savings in observer gain calculations. The proposed scheme ensures that the derivative of the estimated position is indeed the estimate of the velocity component and to achieve such a result, a parameter-dependent Lyapunov function was utilized to ensure the asymptotic convergence of the state estimation error.

A new actuator activation policy for performance enhancement of controlled diffusion processes

The present work aims at the development of a framework within which a moving actuator activation policy and feedback controller synthesis are integrated for diffusion processes modelled by parabolic partial differential equations. It is assumed that the process of interest has either: (i) multiple actuators and the desirable arrangement is to activate only one while keeping the remaining ones dormant, or (ii) a single actuator capable of moving at a priori selected positions within the spatial domain. Practical advantages associated with arrangement (i) are energy cost savings and simplification of the local controller synthesis and the overall switching scheme, and with (ii) is enhanced spatiotemporal disturbance compensation. Feedback controller synthesis methods based on linear matrix inequality techniques are employed for a finite-dimensional Galerkin approximation of the original distributed parameter system. Along with standard controllability criteria, additional conditions are imposed that ensure robustness with respect to a certain class of disturbances. The value of a performance functional is then explicitly calculated by solving a location-parameterized family of Lyapunov matrix equations, and then optimized with respect to the set of admissible actuator locations. Finally, a case study of a moving bed adsorber is presented where the performance-enhancing capabilities of the proposed method is evaluated through simulation studies.

Synchronization and consensus controllers for a class of parabolic distributed parameter systems

Abstract This work examines the consensus control problem for a class of partial differential equations with a Riesz-spectral state operator. The objective is to design controllers that ensure that the state of each of the N systems agrees with the remaining states and at the same time achieves the control objectives of tracking or regulation. Both the case of full state and partial state availability are considered and in the special case of Riesz-spectral operators, one can obtain an explicit bound on the convergence rate of the pairwise state errors. The results are also extended to the case where the all-to-all connectivity among the N systems assumption is relaxed. Extensive numerical studies provide a further insight on the effects of consensus control.

Integrated Actuator–Sensor Placement and Hybrid Controller Design of Flexible Structures Under Worst Case Spatiotemporal Disturbance Variations

The aim of this study is to propose a methodology for placing actuating devices in flexible structures that, in addition to possible modal controllability and enhanced performance, may also address spatiotemporal effects of disturbances. The resulting actuator locations enhance the controllability properties of selected modes, improve the performance of the closed-loop system by integrating the controller design and actuator location, and finally address the spatial variability of disturbances by minimizing the location-parameterized norm of an associated transfer function. When the spatial distribution of disturbances is known a priori, it should be utilized in the placement criteria, and if it is unknown, then a “worst” such distribution may be assumed and subsequently used for actuator placement in order to attain spatial robustness. To further address possible “moving” disturbances, where the spatial distribution of disturbances is changing with time and space, a supervisory scheme is proposed where both an actuator and its associated controller are chosen to be activated (switched in) from a set of candidate actuators that are optimally mounted on the flexible structure. Extensive simulation studies demonstrating the effects of spatial distributions of disturbances on the actuator locations, along with a switching actuator–controller scheme to better address the effects of spatiotemporally varying disturbances, are included.