Higher-order sliding mode stabilization for a class of nonholonomic perturbed systems

Integral sliding mode control of an extended Heisenberg system

“…The presence of the uncertainties in the right-hand side makes the class of systems different from the one considered in [12,15]. Furthermore, in these works (and also in [11,13]), discontinuous controllers were designed leading to the stabilization of chained systems, with or without dynamical extension. However, the system (10)-(12) cannot always be transformed in the chained form with additional integrators.…”

“…In many works about the stabilization of the Heisenberg system [7,8,10] (or, in general, about the stabilization of nonholonomic systems [11,12,13]), the derived control laws are of discontinuous type and can lead to discontinuous velocities in practice. This difficulty can be overcome by adding cascade integrators in the path of the usual control inputs so that the discontinuous part of the control is embedded in higher time derivatives of the variables associated to the mechanical parts.…”

“…Therefore, an important issue for a practical control design is the robustness consideration. Most of robust stabilization results and investigations focus on the stabilization of chained form systems with matched uncertainties [13] (perturbations that enter the state equation at the same point as the control input), with sensor noise and external disturbances [12,14,15].…”

Missile Interceptor Guidance and Control Using Second Order Sliding Modes

“…This situation calls for the integrated design of all interceptor modules: sensor information processing and necessary data estimation, a homing guidance law, and flight control (autopilot). The primary goal of this work is to develop the enabling guidance and control technology for missile interceptors to achieve the hit-to-kill accuracy against targets performing evasive maneuvers including spiralling motion, using high order sliding mode control (HOSM) developed in works of Floquet, Barbot, & Perruquetti (2003), Fridman (2001Fridman ( , 2003, Levant (1993Levant ( ,1998Levant ( , 2001Levant ( , 2003, and Orlov, Aguilar, & Cadiou (2003). The main concern of the paper is to use minimum possible information in order to achieve the goal (target intercept) in presence of uncertainties and disturbances acting in the homing loop.…”

Finite-time output stabilization of the double integrator

“…The reader may found additional properties and results on homogeneity in [6], [7], [8], [9], [10]. The homogeneity property was used many times to design FTS state controls [11], [12], [13], [14], [15], [16], FTS observers [17], [18] and FTS output feedback [19], [20].…”