Asymptotic Disturbance Rejection for Hammerstein Positive Real Systems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57797/1/HarshadHammerPRTCST2003.pd

Retrospective Cost Adaptive NARMAX Control of Hammerstein Systems with Ersatz Nonlinearities

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106496/1/AIAA2013-4851.pd

Control of multivariable Hammerstein systems by using feedforward passivation

This paper presents a new control method for processes which can be described by Hammerstein models. The control design is based on the concept of passive systems. The proposed method is based on feedforward passivation and thus can be applied to nonminimum phase processes and/or processes of high relative degree. A synthesis technique for marginally stable positive real systems has been developed to achieve offset free control. The new control design can be easily implemented by solving a set of linear matrix inequalities. The proposed approach is illustrated using the example of an acid-base pH control problem

Adaptive control with convex saturation constraints

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/166259/1/cth21096.pd

Adaptive Input Reconstruction with Application to Model Refinement, State Estimation, and Adaptive Control.

Input reconstruction is the process of using the output of a system to estimate its input. In some cases, input reconstruction can be accomplished by determining the output of the inverse of a model of the system whose input is the output of the original system. Inversion, however, requires an exact and fully known analytical model, and is limited by instabilities arising from nonminimum-phase zeros. The main contribution of this work is a novel technique for input reconstruction that does not require model inversion. This technique is based on a retrospective cost, which requires a limited number of Markov parameters. Retrospective cost input reconstruction (RCIR) does not require knowledge of nonminimum-phase zero locations or an analytical model of the system. RCIR provides a technique that can be used for model refinement, state estimation, and adaptive control. In the model refinement application, data are used to refine or improve a model of a system. It is assumed that the difference between the model output and the data is due to an unmodeled subsystem whose interconnection with the modeled system is inaccessible, that is, the interconnection signals cannot be measured and thus standard system identification techniques cannot be used. Using input reconstruction, these inaccessible signals can be estimated, and the inaccessible subsystem can be fitted. We demonstrate input reconstruction in a model refinement framework by identifying unknown physics in a space weather model and by estimating an unknown film growth in a lithium ion battery. The same technique can be used to obtain estimates of states that cannot be directly measured. Adaptive control can be formulated as a model-refinement problem, where the unknown subsystem is the idealized controller that minimizes a measured performance variable. Minimal modeling input reconstruction for adaptive control is useful for applications where modeling information may be difficult to obtain. We demonstrate adaptive control of a seeker-guided missile with unknown aerodynamics.Ph.D.Aerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91520/1/amdamato_1.pd

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems

Observer-based H∞ control for systems with repeated scalar nonlinearities and multiple packet losses

This paper is concerned with the H∞ control problem for a class of systems with repeated scalar nonlinearities and multiple missing measurements. The nonlinear system is described by a discrete-time state equation involving a repeated scalar nonlinearity, which typically appears in recurrent neural networks. The measurement missing phenomenon is assumed to occur, simultaneously, in the communication channels from the sensor to the controller and from the controller to the actuator, where the missing probability for each sensor/actuator is governed by an individual random variable satisfying a certain probabilistic distribution in the interval [0 1]. Attention is focused on the analysis and design of an observer-based feedback controller such that the closed-loop control system is stochastically stable and preserves a guaranteed H∞ performance. Sufficient conditions are obtained for the existence of admissible controllers. It is shown that the controller design problem under consideration is solvable if certain linear matrix inequalities (LMIs) are feasible. Three examples are provided to illustrate the effectiveness of the developed theoretical result

Retrospective Cost Adaptive Control of Uncertain Hammerstein Systems.

This dissertation extends retrospective cost adaptive control (RCAC) by broadening its applicability to nonlinear systems. Specifically, we consider command following and disturbance rejection for uncertain Hammerstein systems. All real-world control systems must operate subject to constraints on the allowable control inputs. We use convex optimization to perform the retrospective input optimization, provided the saturation levels are known. The use of convex optimization bounds the magnitude of the retrospectively optimized input and thereby influences the controller update to satisfy the control bounds. We demonstrate this technique on illustrative numerical examples involving single and multiple inputs. In particular, this technique is applied to a multi-rotor helicopter with constraints on the total thrust magnitude and inclination of the rotor plane. We develop RCAC for uncertain Hammerstein systems with odd, even, or arbitrary nonlinearities by constructing auxiliary nonlinearities to account for the non-monotonic input nonlinearities. The purpose of the auxiliary nonlinearities is to ensure that RCAC is applied to a Hammerstein system with a globally nondecreasing composite input nonlinearity. We assume that the linear plant is either asymptotically stable or minimum-phase, and only one Markov parameter of the linear plant is known. The input nonlinearity is uncertain. The required modeling information for the input nonlinearity includes the intervals of monotonicity as well as values of the nonlinearity that determine overlapping segments of the range of the nonlinearity within each interval of monotonicity. Although RCAC is able to tune the linear controller to the command signal and nonlinear characteristics of the plant, the ability of the linear controller to produce accurate command following is limited by the distortion introduced by the nonlinearities. The linear controller structure of RCAC is replaced by a NARMAX (nonlinear ARMAX) controller structure, where the basis functions in the NARMAX controller are chosen by the user, and the controller coefficients appear linearly. To account for the case in which the input nonlinearity is uncertain, we investigate the performance of retrospective cost adaptive NARMAX control (RCNAC) in the case of uncertainty, an approximate input nonlinearity, called the ersatz nonlinearity, can be used by RCANC for adaptation.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/100042/1/yanjin_1.pd