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This paper considers the identifiability problem for a model given by aerospace domain describing aircraft dynamics with time delays. Analytic and algebraic approaches are used to show how different approximations derived from the original non linear and retarded system may result in different identifiability conclusions.
In this paper theorem of an algebraic identity that rewrites a product of n variables as additions of n th power functions is introduced. Theorem of a representation of continuous functions of many variables is provided as an application of theorem of the algebraic identity. Theorem of piecewise linear (PWL) enclosures (having representable lower and upper bounds) of continuous functions is provided...
Recent results in the study of the Hamilton Jacobi Bellman (HJB) equation have led to the discovery of a formulation of the value function as a linear Partial Differential Equation (PDE) for stochastic nonlinear systems with a mild constraint on their disturbances. This has yielded promising directions for research in the planning and control of nonlinear systems. This work proposes a new method obtaining...
In this paper we construct high-order approximate solutions to the value function and optimal control for a finite-horizon optimal control problem for time-varying discrete-time nonlinear systems. The method consists in expanding the dynamic programming equations (DPE) in a power series, collecting homogeneous polynomial terms and solving for the unknown coefficients from the known and previously...
In this paper an observer for a polynomial nonlinear (nonautonomous) system constrained to a bounded subset of the state space is considered. The presented approach allows the construction of a locally asymptotically stable observer, which is guaranteed to be stable for any possible state within the limits. It is based on a theorem of Jacobi and Prestel. The problem is rewritten as an optimization...
A simple, well-interpretable, and explicit analytical solution to the Burgers equation based on Volterra series is derived. Its region of convergence is investigated and a method for the computationally efficient numerical evaluation of the associated Volterra polynomials is presented. For a given boundary condition, numerical results are compared to a widely-used numerical standard solution. After...
This paper addresses nonlinear nonstationary system identification from stimulus-response data, a problem concerning a large variety of applications, in dynamic control as well as in signal processing, communications, physiological system modelling and so on. Among the different methods suggested in the vast literature for nonlinear system modelling, the ones based on the Volterra series and the Neural...
In this contribution, multiple-input multiple-output (MIMO) mixing systems are considered, which are instantaneous and nonlinear but polynomial. We first address the problem of invertibility, searching the inverse in the class of polynomial systems. It is shown that Grobner bases techniques offer an attractive solution for testing the existence of an exact inverse and computing it. By noticing that...
This paper proposes to identify a nonlinear system in the nonlinear ARX model from input-output data. A local linear ARX model identification is done by selecting the input and output data around the selected level. By integrating the local linear ARX models, a nonlinear ARX model with parameters nonlinearly depending on the input and output is identified. The dependence of parameters on the input...
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