Central suboptimal H∞ filtering for nonlinear polynomial systems with multiplicative noise
ABSTRACT This paper presents the central finite-dimensional H∞ filter for nonlinear polynomial systems with multiplicative noise, that is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the original H∞ filtering problem to the corresponding optimal H2 filtering problem, using the technique proposed in . The paper presents the central suboptimal H∞ filter for the general case of nonlinear polynomial systems with multiplicative noise, based on the optimal H2 filter given in . The central suboptimal H∞ filter is also derived in a closed finite-dimensional form for third (and less) degree polynomial system states. Numerical simulations are conducted to verify performance of the designed central suboptimal filter for nonlinear polynomial systems against the central suboptimal H∞ filters available for polynomial systems with state-independent noise and the corresponding linearized system.
- Neurocomputing 01/2015; 148:512-520. · 2.01 Impact Factor
- [Show abstract] [Hide abstract]
ABSTRACT: This paper presents a solution to a robust optimal regulation problem for a nonlinear polynomial system affected by parametric and matched uncertainties, which is based only on partial state information. The parameters describing the dynamics of the nonlinear polynomial plant depend on a vector of unknown parameters, which belongs to a finite parametric set, and the application of a certain control input is associated with the worst or least favourable value of the unknown parameter. A high-order sliding mode state reconstructor is designed for the nonlinear plant in such a way that the previously designed control can be applied for a system with incomplete information. Additionally, the matched uncertainty is also compensated by means of the same output-based regulator. The obtained algorithm is applied to control an uncertain nonlinear inductor circuit of the third order and a mechanical pendulum of the third order, successfully verifying the effectiveness of the developed approach.International Journal of Systems Science 01/2014; 45(9). · 1.58 Impact Factor
- [Show abstract] [Hide abstract]
ABSTRACT: This paper deals with the problem of reliable H ∞ filtering for a class of switched discrete-time time-delay systems with sensor failures by utilizing the multiple Lyapunov functions method and an estimated state-dependent switching technique. We require neither the stability of each individual subsystem nor the measurability of the system states. A switching rule depending on the filter states is designed, which, together with the filter, can guarantee that switched filtering error systems achieve asymptotic stability and with H ∞ performance γ for all possible sensor failures. In sufficient conditions, we introduce some additional scalar matrix variables to realize the decoupling between the filtering error system matrices and Lyapunov matrices. The reliable H ∞ filter gains can be obtained by solving LMIs. Finally, two illustrative examples are provided to demonstrate the feasibility of the theoretical results.Journal of the Franklin Institute 01/2013; 350(10). · 2.26 Impact Factor