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...

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...

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.

This paper gives necessary and sufficient conditions under which an affine nonlinear system is feedback equivalent to a port controlled Hamiltonian system. In particular, we identify the minimum number of linear partial differential equations that need to be solved to achieve this transformation. Copyright c ©2005 IFAC.

In this lecture, we investigate the existence of a state feedback control and a change of coordinates that transform a nonlinear control system affine in the inputs into an equivalent linear system. The treatment corresponds to selected parts from Chapter 9 in [1], Chapter 13 in [2], and Chapter 4 in [3].

In order to approximate any nonlinear system, not just affine nonlinear systems, generalized T-S fuzzy systems, where the control variables and the state variables, are all premise variables are introduced in the paper. Firstly, fuzzy spaces and rules were determined by using ant colony algorithm. Secondly, the state-space model parameters are identified by using genetic algorithm. The simulati...

Control system design for complex nonlinear systems has been widely studied in the last decade. Many remarkable results in this area have been reported, including feedback linearization techniques (Isidori 1989, Esfandiari and Khalil 1992), backstepping design (Krstic et al. 1995) for systems with unmatched uncertainties (Koshkouei et al. 2004). For uncertain systems, sliding mode control appro...

This paper presents a novel method to enhance the performance of traditional speaker adaptation algorithm using discriminative adaptation procedure based on a novel confidence measure and non-linear weighting. Regardless of the distribution of the adaptation data, traditional model adaptation methods incorporate the adaptation data undiscriminatingly. When the data size is small and the paramet...

This paper deals with piecewise affine (PWA) approximation of nonlinear systems. Its motivation is simple. If the controlled plant exhibits nonlinear behavior, linear controller based on linearized model may often be unable to achieve satisfactory performance. On the other hand, intrinsic complexity of the nonlinear controller based on full nonlinear model may prevent it from practical applicat...