Adaptive Observer Design for Nonlinear Interconnected Systems With Applications

In this chapter, observers are designed for a class of nonlinear interconnected systems with uncertain TVPs, in which both the isolated subsystems and the interconnections are nonlinear. The designed observers are variable structure interconnected systems, but may not result in sliding motion. Under the condition that the difference between the unknown TVPs and the corresponding uncertain nominal values are bounded by constants, adaptive updating laws are proposed to estimate the parameters. The persistence of excitation conditions is not required. A set of sufficient conditions are proposed such that the error dynamics formed by the system states and the designed observers are asymptotically stable, while the parameters’ estimation errors are uniformly, ultimately bounded using the LaSalle’s theorem. The results obtained are applied to a coupled inverted pendulum system, and simulation results are presented to demonstrate the effectiveness and feasibility of the developed results. The main contribution includes: (i) Both the interconnections and isolated subsystems take nonlinear forms. (ii) The unknown parameters considered in the system are time varying, and the corresponding nominal values are not required to be known. (iii) The asymptotic convergence of the observation error between the states of the considered systems and the states of the designed observers is guaranteed; while the estimate errors of the TVPs are uniformly, ultimately bounded

Adaptive Sliding Mode Observer for Nonlinear Interconnected Systems with Time Varying Parameters

In this paper, a class of nonlinear interconnected systems with uncertain time varying parameters (TVPs) is considered. Both the interconnections and the isolated subsystems are nonlinear. Sliding mode control method and adaptive techniques are employed together to design an observer to estimate the state variables of the systems in presence of unknown TVPs. The Lyapunov direct method is used to analysis the stability of the sliding motion and it is not required to solve the so-called constrained Lyapunov problem (CLP). A set of conditions is developed under which the augmented systems formed by the error dynamical systems and the designed adaptive laws, are globally uniformly ultimately bounded. A simulation example is presented and the results show that the method proposed in this paper is effective

Transition control based on grey, neural states

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Model Identification and Adaptive State Observation for a Class of Nonlinear Systems

In this article, we consider the joint problems of state estimation and model identification for a class of continuous-time nonlinear systems in the output-feedback canonical form. An adaptive observer is proposed that combines an extended high-gain observer and a discrete-time identifier. The extended observer provides the identifier with a dataset permitting the identification of the system model and the identifier adapts the extended observer according to the new estimated model. The design of the identifier is approached as a system identification problem and sufficient conditions are presented that, if satisfied, allow different identification algorithms to be used for the adaptation phase. The cases of recursive least-squares and multiresolution black-box identification via wavelet-based identifiers are specifically addressed. Stability results are provided relating the asymptotic estimation error to the prediction capabilities of the identifier. Robustness with respect to additive disturbances affecting the system equations and measurements is also established in terms of an input-to-state stability property relative to the noiseless estimates

Adaptive Kalman Filter for Actuator Fault Diagnosis

International audienceAn adaptive Kalman filter is proposed in this paper for actuator fault diagnosis in discrete time stochastic time varying systems. By modeling actuator faults as parameter changes, fault diagnosis is performed through joint state-parameter estimation in the considered stochastic framework. Under the classical uniform complete observability-controllability conditions and a persistent excitation condition, the exponential stability of the proposed adaptive Kalman filter is rigorously analyzed. The minimum variance property of the combined state and parameter estimation errors is also demonstrated. Numerical examples are presented to illustrate the performance of the proposed algorithm

Regelungstheorie

The workshop “Regelungstheorie” (control theory) covered a broad variety of topics that were either concerned with fundamental mathematical aspects of control or with its strong impact in various fields of engineering

Neural Stochastic Contraction Metrics for Learning-based Control and Estimation

We present Neural Stochastic Contraction Metrics (NSCM), a new design framework for provably-stable learning-based control and estimation for a class of stochastic nonlinear systems. It uses a spectrally-normalized deep neural network to construct a contraction metric and its differential Lyapunov function, sampled via simplified convex optimization in the stochastic setting. Spectral normalization constrains the state-derivatives of the metric to be Lipschitz continuous, thereby ensuring exponential boundedness of the mean squared distance of system trajectories under stochastic disturbances. The trained NSCM model allows autonomous systems to approximate optimal stable control and estimation policies in real-time, and outperforms existing nonlinear control and estimation techniques including the state-dependent Riccati equation, iterative LQR, EKF, and the deterministic NCM, as shown in simulation results

Multi-Rate Observers for Model-Based Process Monitoring

Very often, critical quantities related to safety, product quality and economic performance of a chemical process cannot be measured on line. In an attempt to overcome the challenges caused by inadequate on-line measurements, state estimation provides an alternative approach to reconstruct the unmeasured state variables by utilizing available on-line measurements and a process model. Chemical processes usually possess strong nonlinearities, and involve different types of measurements. It remains a challenging task to incorporate multiple measurements with different sampling rates and different measurement delays into a unified estimation algorithmic framework. This dissertation seeks to present developments in the field of state estimation by providing the theoretical advances in multi-rate multi-delay observer design. A delay-free multi-rate observer is first designed in linear systems under asynchronous sampling. Sufficient and explicit conditions in terms of maximum sampling period are derived to guarantee exponential stability of the observer, using Lyapunov’s second method. A dead time compensation approach is developed to compensate for the effect of measurement delay. Based on the multi-rate formulation, optimal multi-rate observer design is studied in two classes of linear systems where optimal gain selection is performed by formulating and solving an optimization problem. Then a multi-rate observer is developed in nonlinear systems with asynchronous sampling. The input-to-output stability is established for the estimation errors with respect to measurement errors using the Karafyllis-Jiang vector small-gain theorem. Measurement delay is also accounted for in the observer design using dead time compensation. Both the multi-rate designs in linear and nonlinear systems provide robustness with respect to perturbations in the sampling schedule. Multi-rate multi-delay observer is shown to be effective for process monitoring in polymerization reactors. A series of three polycondensation reactors and an industrial gas-phase polyethylene reactor are used to evaluate the observer performance. Reliable on-line estimates are obtained from the multi-rate multi-delay observer through simulation