34 research outputs found
Efficient LMI-based quadratic stabilization of interval LPV systems with noisy parameter measures
none2openL. IETTO; Valentina OrsiniIetto, Leopoldo; Orsini, Valentin
On characterisations of the input to state stability properties for conformable fractional order bilinear systems
This paper proposes for the first time the theoretical requirements that a fractional-order bilinear system with conformable derivative has to fulfil in order to satisfy different input-to-state stability (ISS) properties. Variants of ISS, namely ISS itself, integral ISS, exponential integral ISS, small-gain ISS, and strong integral ISS for the general class of conformable fractional-order bilinear systems are investigated providing a set of necessary and sufficient conditions for their existence and then compared. Finally, the correctness of the obtained theoretical results is verified by numerical example
Nonlinear robust H∞ control.
A new theory is proposed for the full-information finite and infinite horizontime
robust H∞ control that is equivalently effective for the regulation and/or tracking
problems of the general class of time-varying nonlinear systems under the presence of
exogenous disturbance inputs. The theory employs the sequence of linear-quadratic and
time-varying approximations, that were recently introduced in the optimal control
framework, to transform the nonlinear H∞ control problem into a sequence of linearquadratic
robust H∞ control problems by using well-known results from the existing
Riccati-based theory of the maturing classical linear robust control. The proposed
method, as in the optimal control case, requires solving an approximating sequence of
Riccati equations (ASRE), to find linear time-varying feedback controllers for such
disturbed nonlinear systems while employing classical methods. Under very mild
conditions of local Lipschitz continuity, these iterative sequences of solutions are
known to converge to the unique viscosity solution of the Hamilton-lacobi-Bellman
partial differential equation of the original nonlinear optimal control problem in the
weak form (Cimen, 2003); and should hold for the robust control problems herein. The
theory is analytically illustrated by directly applying it to some sophisticated nonlinear
dynamical models of practical real-world applications. Under a r -iteration sense, such
a theory gives the control engineer and designer more transparent control requirements
to be incorporated a priori to fine-tune between robustness and optimality needs. It is
believed, however, that the automatic state-regulation robust ASRE feedback control
systems and techniques provided in this thesis yield very effective control actions in
theory, in view of its computational simplicity and its validation by means of classical
numerical techniques, and can straightforwardly be implemented in practice as the
feedback controller is constrained to be linear with respect to its inputs
Lyapunov Theorems for Systems Described by Retarded Functional Differential Equations
Lyapunov-like characterizations for non-uniform in time and uniform robust
global asymptotic stability of uncertain systems described by retarded
functional differential equations are provided
Nonlinear Tracking Control Using a Robust Differential-Algebraic Approach.
This dissertation presents the development and application of an inherently robust nonlinear trajectory tracking control design methodology which is based on linearization along a nominal trajectory. The problem of trajectory tracking is reduced to two separate control problems. The first is to compute the nominal control signal that is needed to place a nonlinear system on a desired trajectory. The second problem is one of stabilizing the nominal trajectory. The primary development of this work is the development of practical methods for designing error regulators for Linear Time Varying systems, which allows for the application of trajectory linearization to time varying trajectories for nonlinear systems. This development is based on a new Differential Algebraic Spectral Theory. The problem of robust tracking for nonlinear systems with parametric uncertainty is studied in relation to the Linear Time Varying spectrum. The control method presented herein constitutes a rather general control strategy for nonlinear dynamic systems. Design and simulation case studies for some challenging nonlinear tracking problems are considered. These control problems include: two academic problems, a pitch autopilot design for a skid-to-turn missile, a two link robot controller, a four degree of freedom roll-yaw autopilot, and a complete six degree of freedom Bank-to-turn planar missile autopilot. The simulation results for these designs show significant improvements in performance and robustness compared to other current control strategies