State-dependent parameter models of non-linear sampled-data systems: a velocity-based linearization approach

Characterization of semiglobal stability properties for discrete-time models of non-uniformly sampled nonlinear systems

Extended State Dependent Parameter modelling with a Data-Based Mechanistic approach to nonlinear model structure identification

Linear regressive realizations of LTI state space models

Ahlstrom Corp, Finland

In this paper, a least-mean-squares (LMS) finite memory (FM) estimator for a stochastic discrete-time state space model is obtained by taking the conditional expectation of the estimated state given a finite number of inputs and outputs measured on the recent finite horizon. Any a priori state information is not involved and any arbitrary constraints are not imposed. For a general discrete-time state space model with both system and measurement noises, the LMS FM estimator is represented in a closed-form. It turns out that the proposed LMS FM estimator has the unbiased property and the linear structure with respect to inputs and outputs on the recent finite horizon.

In this paper, we treat the problem of decentralized implicit adaptive regulation for large-scale stochastic systems composed into a set of interconnected systems that are described by discrete-time state-space mathematical models with unknown parameters. The key idea in the decentralized regulation method is to design local regulator using only local information such that the state of each interconnected system is regulated to a certain constant reference signal. The main contribution is the proposition of a decentralized implicit adaptive regulator based on state-feedback strategy that can be applied to stochastic interconnected systems with unknown parameters. Furthermore, the practical implementation of the proposed decentralized implicit adaptive regulator can be made easily (low-cost implementation of the electronic components, short computation of the decentralized control law, etc.). A theorem is established and proved which gives sufficient stability conditions of the resulting closed-loop interconnected systems by using the Lyapunov method. An example of numerical simulation is treated to test the performance of the proposed decentralized implicit adaptive regulator.

In this article, input-to-state stability (ISS) and stabilization are examined for sampled-data systems under deterministic aperiodic sampling and random sampling, respectively. Using the direct design method, the sampled-data systems are transformed into switched systems with switched time-varying delays. First, the ISS definition and criterion appropriate for these systems are provided. Based on this, the ISS criterion on sampled-data systems under deterministic aperiodic sampling is given. Second, after the stochastic ISS (SISS) definition and criterion are provided for switched nonlinear systems with randomly switching delays, the SISS criterion for the sampled-data systems under random sampling is provided. All of the ISS and SISS definitions are given in the form of $\mathcal {KL}$ function that is quite elegant and easy to work with. Then, sufficient conditions for input-to-state stabilization are obtained for sampled-data linear systems under deterministic aperiodic sampling and random sampling, respectively, via the Lyapunov-Krasovskii method. Finally, based on the criteria, a piecewise controller is designed by the matrix inequality approach for a sampled-data linear time invariant system, and simulation results are provided to illustrate our design method. The main conclusion of this article is that sampling intervals will affect the controller design of the systems, and the ISS properties are maintained using a piecewise controller.

In this paper, a reduced-order modeling approach based on computational fluid dynamics is presented for an elastic wing with control surfaces in the transonic regime. To treat the computational fluid dynamics grid around the geometrical discontinuities, due to the deflection of control surfaces, the constant volume tetrahedron method and the transpiration method are combined together without deforming the grid. Based on the input–output data from the computational fluid dynamics solver, one multiple-input/multiple-output discrete-time state-space model for the wing is identified via a robust subspace algorithm. For each control surface, one one-input/multiple-output discrete-time state-space model is identified using the same algorithm. With the precomputed state-space models for a few flight parameters, the generalized aerodynamic forces over a range of flight parameters can be computed by interpolating the output data. The methodology is applied to an elastic wing model with two control surfaces...

Suboptimal Control of Nonlinear Dynamic System with Unlimited Transition Process Time

Many of nonlinear control systems are sampled-data system, i.e. the continuous-time nonlinear plants are controlled by digital controllers. So it is important to investigate that if the solution of the discrete-time output regulation problem is effective to sampled-data nonlinear control systems. Recently a feedforward neural network based approach to solving the discrete regulator equations has been presented. This approach leads to an effective way to practically solve the discrete nonlinear output regulation problem. In this paper the approach is used to sampled-data nonlinear control system. The simulation of the sampled-data system shows that the control law designed by the proposed approach performs much better than the linear control law does.

A connection between multi-linear and Volterra systems

This paper focuses on the parameter estimation of multi-input multi-output (MIMO), linear time-periodic (LTP) systems in the time domain. Discrete-time state-space models are selected for the description of LTP systems and the Covariance Based Realization Algorithm (CoBRA), one branch of subspace methods, is used for the identification of the generalized time-lifted state-space model for an LTP system. The use of the CoBRA method for estimation is motivated by the robustness against output noise with (high-order) noise dynamics and a focus on the estimation of low rank deterministic model for the LTP system. In addition to the use of CoBRA, a novel method is proposed to compute a topologically equivalent realization for the original LTP system. The method includes two different but theoretically equivalent approaches of calculating the state matrices, which can be also used as a measure for the estimation quality. Finally, a simulation is given to illustrate the efficiency of the proposed method.

An optimal tracking control of a heat exchanger with load change is considered. It is assumed that the plant is described by a discrete-time state-space model with time-delay, and a direct link between input and output. First, based on the linear quadratic inverse technique, the authors derive an optimal tracking controller having integral, state feedback plus preview actions. To derive a state-space model of a heat exchanger, an ARX model was fitted to the open-loop data obtained from the plant. The properties of the tracking control algorithm are analyzed by simulation studies using the identified model. The optimal control algorithm with an observer was installed on a process computer to provide the set points for the analog PID (proportional plus integral plus derivative) regulators of a heat exchanger plant. Experimental studies show that the control performance of water outlet temperature in the presence of load change is greatly improved.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust [formula omitted] observer design for sampled-data Lipschitz nonlinear systems with exact and Euler approximate models

A unified analytic approach is presented for the design of adaptive sampling control law in sampled-data systems. This is accomplished by introducing an objective function which measures the performance of the sampler over each sampling interval, and then minimize it to obtain the sampling control law. A total of six different control laws, which are functions of the sampled function, are derived from the generalized objective function by selecting different weighting coefficients. More than half of these control laws are identical to existing results. Similar control laws as functions of the system output can be derived as well. Also included are some experimental results on the performances of four representative control laws in a second-order system subject to step disturbance.