Decentralized Control Synthesis for Interconnected LTV Systems using Shifted Legendre Polynomials

A direct method based on using shifted Legendre polynomials is developed to obtain suboptimal control for linear time-varying systems with multiple state and control delays and quadratic performance index. In this method, both the control and state variables are first expanded into finite shifted Legendre series. The governing delay-differential equation is then converted to a set of linear algebraic equations through use of the operational matrices of integration and delay. The problem finally becomes the simple one of finding the unknown coefficients of the control variables alone, which minimizes the quadratic form of performance index.

The paper presents a new approach to the solution of the problem of disturbances attenuation for interconnected dynamic systems by using decentralized control, such that the effect of the disturbances on the whole system is reduced to a required acceptable level. A class of uncertain, nominally linear interconnected continuoustime systems including both non-delayed and delayed inputs under unknown but norm-bounded parameter uncertainties described in the state space is considered. A decentralized, memoryless H ∞ control is designed by using the Riccati equation approach. The feedback control law guarantees the asymptotic stability of the overall closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed level. The study of the case control design for a building structure under earthquakes excitation is presented. Though various solutions dealing with the problem of structural input delayed control appear in the literature [1], [8], [10], [13], this problem has not been solved yet[2]-[7], [11], [12], [15].

In this work, a general class of pantograph type nonlinear fractional integro-differential equations (PT-FIDEs) with non-singular and non-local kernel is considered. A numerical scheme based on the orthogonal basis functions including the shifted Legendre polynomials (SLPs) is proposed. First, we expand the unknown function and its derivatives in terms of the SLPs with unknown coefficients. Then, we present several theorems based on the SLPs for the help to achieve the approximate solution of the problem under study. Finally, by utilizing these theorems together with the collocation points, the main problem is transformed to a system of linear or nonlinear algebraic equations, which can be simply solved. An investigation for error estimate is discussed. The accuracy and efficiency of the proposed scheme are reported by four illustrative examples.

For linear time-varying single-input single-output systems, the paper treats the problem of designing an output feedback controller resulting in an (internally) stable closed-loop system that tracks a given reference signal. The design is accomplished by augmenting the given system to include an internal model of the reference signal. The internal model reduces to the usual form when the given plant is time invariant. An explicit construction for the internal model is given in the case of a step reference.

The frequency-domain concept of diagonal dominance, as defined by Rosenbrock, is sensitive to changes in the scaling of the system input and output variables. Mees has determined an optimal constant diagonal scaling matrix such that the resulting system is as near dominant as possible at a particular frequency. Also, Limbeer has further extended Mees result and has shown its relationship to the concepts of 'generalised diagonal dominance' and 'generalised block diagonal dominance'- the latter being of particular interest in the area of decentralised control.

An unsupervised and non-parametric bayesian classifier

The robust H∞ control problem for time-varying uncertain linear systems with time-varying state, and control delays is considered. Based on the Riccati equation approach, we design a robust H∞ linear time-invariant state feedback control law, which stabilizes the system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. A sufficient condition for the existence of the. robust H∞ controller is derived and two synthesis methods are presented for a robust H∞ control law to uncertain time-delay systems. One is to construct a robust H∞ control law by an equivalent linear time-invariant structural description for the sufficient condition and the control law can be obtained by solving an algebraic Riccati equation (ARE). The other method is to transform the sufficient condition into a linear matrix inequality (LMF) problem and the control law can be obtained by solving the LMI. A numerical example is presented to illustrate the obtained results.

Periodic Motions for Estimation of the Attraction Domain in the Wheeled Robot Stabilization Problem

The mean dynamic topography (MDT) can be computed as the difference between the mean sea level (MSL) and a gravimetric geoid. This requires that both data sets are spectrally consistent. In practice, it is quite common that the resolution of the geoid data is less than the resolution of the MSL data, hence, the latter need to be low-pass filtered before the MDT is computed. For this purpose conventional low-pass filters are inadequate, failing in coastal regions where they run into the undefined MSL signal on the conti- nents. In this paper, we consider the use of a bandlimited, spa- tially concentrated Slepian basis to obtain a low-resolution approximation of the MSL signal. We compute Slepian func- tions for the oceans and parts of the oceans and compare the performance of calculating the MDT via this approach with other methods, in particular the iterative spherical harmonic approach in combination with Gaussian low-pass filtering, and various modifications. Based on the numerical experi- ments, we conclude that none of these methods provide a low- resolution MSL approximation at the sub-decimetre level. In particular, we show that Slepian functions are not appropriate basis functions for this problem, and a Slepian representation of the low-resolution MSL signal suffers from broadband leakage. We also show that a meaningful definition of a low- resolution MSL over incomplete spherical domains involves orthogonal basis functions with additional properties that Slepian functions do not possess. A low-resolution MSL signal, spectrally consistent with a given geoid model, is obtained by a suitable truncation of the expansions of the MSL signal in terms of these orthogonal basis functions. We compute one of these sets of orthogonal basis functions using the Gram-Schmidt orthogonalization for spherical harmon- ics. For the oceans, we could construct an orthogonal basis only for resolutions equivalent to a spherical harmonic degree 36. The computation of a basis with a higher resolution fails due to inherent instabilities. Regularization reduces the insta- bilities but destroys the orthogonality and, therefore, pro- vides unrealistic low-resolution MSL approximations. More research is needed to solve the instability problem, per- haps by finding a different orthogonal basis that avoids it altogether.

Numerical solutions of linear time-varying descriptor systems via hybrid functions

Delay-dependent robust and reliable [formula omitted] fuzzy hyperbolic decentralized control for uncertain nonlinear interconnected systems

The issue of fault-tolerant decentralized control is investigated for large-scale civil engineering structures. Considering the correlation of the sub-control system, the sensor failures and the actuator failures, a sufficient condition for decentralized stabilizability is proposed for the class system of discrete-time systems with delay interconnections by using the Lyapunov stability theory and the linear matrix inequality (LMI) approach. It is shown that this condition is equivalent to the feasibility problem of the linear matrix inequality. Furthermore, a decentralized state feedback control law is derived as a convex optimization problem, and the latter can be solved by using existing efficient convex optimization techniques. The obtained controller enables the closed-loop systems to be stable. Considering sensor failures and the actuator failures, the ASCE 9-story benchmark building is selected as a numerical example to evaluate the control performance of the partially independent decentralized control and overlapping decentralized control. Numerical simulation results indicate that the proposed small gain decentralized stabilization control (LMI-SGDSC) algorithm performs as well as the traditional centralized control, and the overlapping decentralized control has a greater level of reliability. The fault tolerant decentralized control (LMI-SGFTDSC) achieves satisfactory control effects.

Decentralized control synthesis using orthogonal functions

The study proposes a new simple output feedback adaptive tracking control scheme using neural network for a class of complicated modern agricultural mechanical systems that only the system output variables can be measured. The scheme avoids design state observer and Lipschiz assumption, SPR conditions are not required and few parameters in control laws and weights update laws need to be tuned. Only one RBF neural network is employed to approximate the lumped uncertain nonlinear function. The stability analysis of the closed-loop system is performing using a Lyapunov approach which shows that the output tracking error and all states in the closed-loop system are boundedness. The effectiveness of the proposed adaptive control scheme is demonstrated through the simulations.

An approach to the design of robust tracking controllers is proposed for a class of large-scale interconnected linear uncertain systems with time-delays. The systems may contain time-delays in both states and controls. With the decentralized controller, the closed-loop system will asymptotically track the reference output. Numerical simulations have demonstrated the effectiveness of the approach proposed.