In this paper, we consider a special class of underactuated mechanical systems with two degrees of freedom and symmetry. By symmetry, we mean the inertia matrix of the system is independent of the unactuated degree of freedom. We show that there exists a natural global change of coordinates obtained from the Lagrangian of the system that transforms the system into a partially linear cascade non...

We present a method for approximating the solution of a parameterized, nonlinear dynamical system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are computed with a nonlinear least squares procedure that minimizes the residual of the governing equations. The approximation properties of this residual mini...

In [1], we have demonstrated that robust optimization of linear finite-horizon control in a discrete time linear dynamical system affected by uncertain disturbances becomes computationally tractable if, rather than using natural parameterization of a linear output-based control law, one passes to a specific re-parameterization of the law, representing it as affine control law based on the so ca...

The problem of estimating unmeasured state and disturbance variables for nonlinear process control applications is considered. We assume that the process model is affine with respect to the unmeasured disturbances and any unmeasured state variables. The disturbances are considered as additional state variables, and a nonlinear observer is designed for the augmented state-space system. The obser...

A gramians based method for quantifying the nonlinearity of the control-affine spatio-temporal systems is proposed in this paper. The empirical gramians are computed from the data collected from a nonlinear model derived by collocation method for spatio-temporal systems. This method compares the empirical gramians of the nonlinear model with that of the linearized model at its steady state oper...

In this paper we develop a theory of stabilizing singleinput nonlinear affine systems using quantized feedback. We construct a stabilizing quantizer based on a control Lyapunov function (CLF), and a robustly stabilizing quantizer based on a robust control Lyapunov function (RCLF). We characterize the coarsest quantizer under certain conditions. The special features of several classes of nonline...

This paper presents a control methodology that enables nonlinear model-based control of pulse width modulated (PWM) pneumatic servo actuators. An averaging approach is developed to describe the equivalent continuous-time dynamics of a PWM controlled nonlinear system, which renders the system, originally discontinuous and possibly nonaffine in the input, into an equivalent system that is both co...

A novel adaptive control approach is proposed to solve the globally asymptotic state stabilization problem for uncertain purefeedback nonlinear systems in the pseudo-affine form. The pure-feedback nonlinear system under consideration is with nonlinearly parameterised uncertainties and possibly unknown control coefficients. Based on the parameter separation technique, a backstepping controller i...

We introduce the concept of an affine flat input to a nonlinear system with a given output function. This approach can be seen as dual to the search for a flat output of a control system with given input. Our results provide a necessary and sufficient condition for the existence of a flat input in the SISO case, which also allows to construct the vector field associated to the flat input. In ad...

Blur in images can be removed by solving a series of box-constrained least-squares problems. In this paper, we compare two recent approaches for solving these problems using affine-scaling methods. Both approaches aim at solving a nonlinear system arising from the Karush-Kuhn-Tucker condition. One approach is to identify the active set and update the inactive components of the iterates by using...