In this paper, we develop an algorithm to compute underand over-approximations to the discrete dynamics of a hybrid automaton. We represent the approximations to the dynamics as sofic shifts, which can be generated by a discrete automaton. We restrict to two-dimensional systems, since these give rise to one-dimensional return maps, which are significantly easier to study. Given generic non-dege...

The paper deals with three different Newton algorithms that have recently been worked out in the general frame of affine invariance. Of particular interest is their performance in the numerical solution of discretized boundary value problems (BVPs) for nonlinear partial differential equations (PDEs). Exact Newton methods, where the arising linear systems are solved by direct elimination, and in...

This paper presents a computational technique that called Tau-collocation method for the developed solution of non-linear integro-differential equations which involves a population model. To do this, the nonlinear integro-differential equations are transformed into a system of linear algebraic equations in matrix form without interpolation of non-poly-nomial terms of equations. Then, using coll...

An interval global optimization method combined with the Direct Method for solving parametric linear systems is used for computing a tight enclosure for the solution set of parametric linear system whose input data are non-linear functions of interval parameters. Revised affine arithmetic is used to handle the nonlinear dependencies. The Direct Method performs the monotonicity test to speed up ...

In this paper, adaptive neural network (NN) control is presented for a class of non-affine nonlinear systems with unknown control gain. Using the Mean Value Theorem and backstepping method, we propose a constructive approach for adaptive NN control design. The Nussbaum function is used to relax the requirement on control direction. The semi-global uniformly ultimately boundedness (SGUUB) of the...

The methods of nonlinear systems and control theory were applied to a simple musculoskeletal system with one joint and two muscles in this paper. For this purpose, a nonlinear input-affine state-space model has been developed for this system with a flexor and an extensor muscle taking into account the nonlinear muscle and movement dynamics. Two types of controllers were designed: a linear pole-...

In this paper, we investigate when passivity for a nonlinear system can be inferred from its linearization. The nonlinear system considered here are affine in control and with feedthrough terms, in both continuous-time domain and discrete-time domain. Our main results demonstrate when the linearized system is simultaneously strict passive and strict input passive (SSIP), the nonlinear system wi...

We present a general formulation for estimation of the region of attraction (ROA) for nonlinear systems with parametric uncertainties using a combination of the polynomial chaos expansion (PCE) theorem and the sum of squares (SOS) method. The uncertain parameters in the nonlinear system are treated as random variables with a probability distribution. First, the decomposition of the uncertain no...

This paper is endeavoured to the problem of local feedback dissipativity and the use of feedback dissipativity for stabilization purposes in the nonlinear discretetime setting. Sufficient conditions under which a class of non-affine discrete-time control systems can be rendered locally dissipative are derived. A methodology in order to render nonlinear single-input single-output discrete-time s...

The problem of output regulation of affine nonlinear systems with the relative degree not well defined by modified steepest descent control is studied. The modified steepest descent control is a dynamic feedback control which is generated by the trajectory following method. By assuming the system is minimum phase, output of the system can be regulated globally asymptotically.