Nonzero Initial State Research Articles

Reachability of nonnegative equilibrium states for the semilinear vibrating string by varying its axial load and the gain of damping

We show that the set of nonnegative equilibrium-like states, namely, like of the semilinear vibrating string that can be reached from any non-zero initial state , by varying its axial load and the gain of damping, is dense in the “nonnegative” part of the subspace of . Our main results deal with nonlinear terms which admit at most the linear growth at infinity in and satisfy certain restriction on their total impact on (0,∞) with respect to the time-variable.

Controllability of the Semilinear Parabolic Equation Governed by a Multiplicative Control in the Reaction Term: A Qualitative Approach

In this paper we are concerned with the global approximate controllability property of a rather general semilinear heat equation with superlinear term, governed in a bounded domain $\Omega \subset R^n$ by a multiplicative (bilinear) control in the reaction term like v u (x,t), where v is the control. We show that any nonnegative target state in $L^2 (\Omega)$ can approximately be reached from any nonnegative, nonzero initial state by applying at most three static bilinear $L^\infty (\Omega)$-controls subsequently in time. This result is further applied to discuss the controllability properties of the nonhomogeneous version of this problem with bilinear term like $v (u (x,t)-\theta (x))$, where $\theta$ is given. Our approach is based on an asymptotic technique allowing us to distinguish and make use of the pure diffusion and/or pure reaction parts of the dynamics of the system at hand, while suppressing the effect of a (general) nonlinear term.

Global non-negative controllability of the semilinear parabolic equation governed by bilinear control

We study the global approximate controllability of the one dimensional semilinear convection-diusion-reaction equation governed in a bounded domain via the coecient (bilinear con- trol) in the additive reaction term. Clearly, even in the linear case, due to the maximum principle, such system is not globally or locally controllable in any reasonable linear space. It is also well known that for the superlinear terms admitting a power growth at innity the global approximate controlla- bility by traditional additive controls of localized support is out of question. However, we will show that a system like that can be steered in L 2 (0; 1) from any non-negative nonzero initial state into any neighborhood of any desirable non-negative target state by at most three static (x-dependent only) above-mentioned bilinear controls, applied subsequently in time, while only one such control is needed in the linear case.

A METHOD FOR COMPUTING LYAPUNOV EXPONENTS SPECTRA WITHOUT REORTHOGONALIZATION

We present a method for the computation of Lyapunov exponents without reorthogon alization. In the low dimension of system(n<5) ,the equations needed in present algorithm is less than those in normal methods such as QR, SVD etc. This method is applicable to both discrete systems and continuous systems, and is still valid when the Lyapunov spectra is degenerate. Numerical analysis to Lorenz dynamical system indicates that the method converges quickly and steadly for arbitrary nonzero initial state.

Fast simulation and sensitivity analysis of lossy transmission lines by the method of characteristics

In this paper we use the method of characteristics to derive a new simulation model of lossy transmission lines, and we present the sensitivity analysis in the time domain. The simulation model is as fast as the recursive convolution model based on moment matching and Pade' approximation, but does not have the stability problem. The sensitivity analysis model is particularly useful for transmission line circuits containing nonlinear elements, and is believed to be the first time domain model. Both the simulation and sensitivity analysis models are applicable to uniform and nonuniform transmission lines with arbitrary nonzero initial states. Also we show that any nonlinear circuit element has a very simple linear model in sensitivity analysis. Furthermore, we demonstrate that for any circuits, the modified nodal admittance (MNA) matrices in simulation and in sensitivity analysis equations are the same, therefore no LU decomposition is needed in sensitivity analysis. The contributions in this paper have been implemented into a general-purpose program CSSC (Circuit Simulation and Sensitivity Analysis with Characteristics) which shows excellent accuracy and efficiency in both simulation and sensitivity analysis of transmission line circuits.

Robust game theoretic synthesis in the presence of uncertain initial states

In this paper a performance robust control synthesis problem is considered; the performance measure v represents the sensitivity of the output to the nonzero initial state. The problem is to find a controller, out of a prescribed set, that minimizes v such that internal stability and a prescribed level of disturbance attenuation for all real parameter uncertainties in a given set are achieved. The primary motivation for considering this problem is that v can be given a direct physical interpretation in terms of the transient response of a closed-loop system. Linear time-invariant systems with output feedback are considered. A game theoretic approach is employed to solve the synthesis problem and necessary conditions for optimality are given.

Design of minimax controllers for linear systems with non‐zero initial states under specified information structures

AbstractIn this paper, we obtain the solution to the discrete‐time, linear‐quadratic, finite‐horizon disturbance rejection problem, with hard bounds on the disturbance and with a known or an unknown non‐zero initial state. It is shown that there exist two regions in the space of initial conditions: one where a pure‐strategy saddle point exists, and the other where no pure‐strategy saddle point exists. In the latter region, the structure of the minimax controller is fixed throughout, and a saddle point exists in the class of mixed policies. The paper also develops a general algorithm for the construction of such saddle points under different information structures, and illustrates this algorithm on a numerical example.

A dynamic games approach to controller design: disturbance rejection in discrete-time

It is shown that the discrete-time disturbance rejection problem, formulated in finite and infinite horizons, and under perfect state measurements, can be solved by making direct use of some results on linear-quadratic zero-sum dynamic games. For the finite-horizon problem an optimal (minimax) controller exists, and can be expressed in terms of a generalized (time-varying) discrete-time Riccati equation. The existence of an optimum also holds in the infinite-horizon case, under an appropriate observability condition, with the optimal control, given in terms of a generalized algebraic Riccati equation, also being stabilizing. In both cases, the corresponding worst-case disturbances turn out to be correlated random sequences with discrete distributions, which means that the problem (viewed as a dynamic game between the controller and the disturbance) does not admit a pure-strategy saddle point. Results for the delayed state measurement and the nonzero initial state cases are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Bist structure using multi-input shift register with initial value

Parallel signature analysers are very useful for compression of test response data for VLSI. In the letter the compression result is obtained from a signature of zeros alone or ones alone from a nonzero initial state, rather than from the traditional method of obtaining a nonzero signature from a zeroed MISR register. An algebraic description of such a signature analysis is given, realised by means of the external exclusive-OR-type MISR.

Imbedding Approach for Optimal Input Design of Linear System Identification

The design of optimal inputs for identifying parameters in MIMO continuous- time linear nonstationary systems with nonzero initial states is considered. The optimal input is shown to be a solution to a Fredholm integral equation of the second kind with a special type of symmetric semi- degenerate kernel subject to an input energy constraint . The solution methods ar e based on invariant imbedding . Initial val ue systems(I.V.S.'s) of the optimal input and the energy constr aint equation are derived for both cases where the coefficient of the energy constrained equation is pre- assigned and where the interval length of identification experiments is specified a priori . The fixed- interval and fixed- point smoothing solutions of the optimal input can be obtained by sol ving each I.V.S. of the optimal input and the total energy with respect to the interval length simultaneously . Some extensions of the results are discussed and a numerical example is shown.