Hybrid robust observers for locally Lipschitz systems

in Proc. European Control Conference, Budapest (2009)

State observer design procedure is proposed for nonlinear locally Lipschitz systems. Possible presence of disturbances is taken into account. The solution is based on logic-based control approach ... [more ▼]

State observer design procedure is proposed for nonlinear locally Lipschitz systems. Possible presence of disturbances is taken into account. The solution is based on logic-based control approach applicable to nonlinear systems with bounded solutions. [less ▲]

Hybrid adaptive observers for locally Lipschitz systems with application to mechanical oscillators

in Proc. IEEE Conf. Control Applications, Saint-Petersburg (2009)

Adaptive observer design procedure is proposed for nonlinear locally Lipschitz systems. Possible presence of disturbances is taken into account. The solution is based on logic-based control approach ... [more ▼]

Adaptive observer design procedure is proposed for nonlinear locally Lipschitz systems. Possible presence of disturbances is taken into account. The solution is based on logic-based control approach applicable to nonlinear systems with bounded solutions. Efficacy of the proposed observer is demonstrated by computer simulation for a mechanical oscil- lating system. [less ▲]

Multigoal Output Regulation Via Supervisory Control: Application to Stabilization of a Unicycle.

in Proc. American Control Conference, St. Louis (2009)

We consider the problem of robust output regulation for nonlinear systems in the following sense: given a system with input disturbances, we are interested in steering one output to zero while tolerating ... [more ▼]

We consider the problem of robust output regulation for nonlinear systems in the following sense: given a system with input disturbances, we are interested in steering one output to zero while tolerating an steady-state error on the second output. In other words, we are interested in input-output (asymptotic) stability for one output and practical (asymptotic) stability for the second. Upon the assumption that we dispose of two controllers each of which achieves separately a control objective (for either output) we propose a switching rule to commute between the two controllers appropriately i.e., conserving the input-output stability, to some extent. The problem studied is reminiscent of different concrete situations such as simultaneaous synchronization and tracking control of mechanical systems; in this article we revisit the problem of stabilizing a unicycle (regulation of the first output) towards a point while ensuring obstacle-collision avoidance (practical stabilization of the second output). [less ▲]

Input-to-output stabilization of nonlinear systems via backstepping

in International Journal of Robust and Nonlinear Control (2009), 19

An extension of a backstepping method for the stabilization of nonlinear systems with respect to a set is presented. Robust control laws providing the system with input-to-output stability are proposed ... [more ▼]

An extension of a backstepping method for the stabilization of nonlinear systems with respect to a set is presented. Robust control laws providing the system with input-to-output stability are proposed. Possibilities of non-strict Lyapunov functions’ application are discussed. The differences between a conventional backstepping method and an approach proposed in Kolesnikov (Synergetic Control Theory. Energoatomizdat: Moscow, 1994; 344) are analyzed. Performance of the obtained solutions is demonstrated by computer simulation for pendulum with an actuator example. [less ▲]

Yakubovich’s Oscillatority of Circadian Oscillations Models

in Mathematical Biosciences (2008), 216

The testing procedure of Yakubovich’s oscillatority property is presented. The procedure is applied for two models of circadian oscillations [10], [11]. Analytical conditions of these models oscillatority ... [more ▼]

The testing procedure of Yakubovich’s oscillatority property is presented. The procedure is applied for two models of circadian oscillations [10], [11]. Analytical conditions of these models oscillatority are established and bounds on oscillation amplitude are calculated. [less ▲]