Alessandro Astolfi

Discontinuous control of nonholonomic systems

The problem of asymptotic convergence for a class of nonholonomic control systems via discontinuous control is addressed and solved from a new point of view. It is shown that control laws, which ensures asymptotic (exponential) convergence of the closed-loop system, can be easily designed if the system is described in proper coordinates. In such coordinates, the system is discontinuous. Hence, the problem of local asymptotic stabilization for a class of discontinuous nonholonomic control systems is dealt with and a general procedure to transform a continuous system into a discontinuous one is presented. Moreover, a general strategy to design discontinuous control laws, yielding asymptotic convergence, for a class of nonholonomic control systems is proposed. The enclosed simulation results show the effectiveness of the method.

Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems

A new method to design asymptotically stabilizing and adaptive control laws for nonlinear systems is presented. The method relies upon the notions of system immersion and manifold invariance and, in principle, does not require the knowledge of a (control) Lyapunov function. The construction of the stabilizing control laws resembles the procedure used in nonlinear regulator theory to derive the (invariant) output zeroing manifold and its friend. The method is well suited in situations where we know a stabilizing controller of a nominal reduced order model, which we would like to robustify with respect to higher order dynamics. This is achieved by designing a control law that asymptotically immerses the full system dynamics into the reduced order one. We also show that in adaptive control problems the method yields stabilizing schemes that counter the effect of the uncertain parameters adopting a robustness perspective. Our construction does not invoke certainty equivalence, nor requires a linear parameterization, furthermore, viewed from a Lyapunov perspective, it provides a procedure to add cross terms between the parameter estimates and the plant states. Finally, it is shown that the proposed approach is directly applicable to systems in feedback and feedforward form, yielding new stabilizing control laws. We illustrate the method with several academic and practical examples, including a mechanical system with flexibility modes, an electromechanical system with parasitic actuator dynamics and an adaptive nonlinearly parameterized visual servoing application.

Homogeneous Approximation, Recursive Observer Design, and Output Feedback

We introduce two new tools that can be useful in nonlinear observer and output feedback design. The first one is a simple extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability and robustness for a homogeneous in the bi-limit vector field. The second tool is a new recursive observer design procedure for a chain of integrator. Combining these two tools, we propose a new global asymptotic stabilization result by output feedback for feedback and feedforward systems.

Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one

We consider the problem of (asymptotic) stabilization of mechanical systems with underactuation degree one. A state-feedback design is derived applying the interconnection and damping assignment passivity-based control methodology. Its application relies on the possibility of solving a set of partial differential equations that identify the energy functions that can be assigned to the closed-loop. The following results are established: 1) identification - in terms of some algebraic inequalities - of a subclass of these systems for which the partial differential equations are trivially solved; 2) characterization of all systems which are feedback-equivalent to this subclass; and 3) introduction of a suitable parametrization of the assignable energy functions that provides the designer with a handle to address transient performance and robustness issues. An additional feature of our developments is that the open-loop system need not be described by a port-controlled Hamiltonian (or Lagrangian) model, a situation that arises often in applications due to model reductions or preliminary feedbacks that destroy the structure. The new result is applied to obtain an (almost) globally stabilizing controller for the inertia wheel pendulum, a controller for the chariot with pendulum system that can swing-up the pendulum from any position in the upper half plane and stop the chariot at any desired location, and an (almost) globally stabilizing scheme for the vertical takeoff and landing aircraft with strong input coupling. In all cases we obtain very simple and intuitive solutions that do not rely on, rather unnatural and technique-driven, linearization or decoupling procedures but instead endows the closed-loop system with a Hamiltonian structure with desired potential and kinetic energy functions.

Spacecraft attitude control using magnetic actuators

The problem of inertial pointing for a spacecraft with magnetic actuators is addressed and an almost global solution to the problem is obtained by means of static attitude and rate feedback. A local solution based on dynamic attitude feedback is also presented. Simulation results demonstrate the practical applicability of the proposed approach.

Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems

The dynamics of many physical processes can be suitably described by Port-Hamiltonian (PH) models, where the importance of the energy function, the interconnection pattern and the dissipation of the system is underscored. To regulate the behavior of PH systems it is natural to adopt a Passivity-Based Control (PBC) perspective, where the control objectives are achieved shaping the energy function and adding dissipation. In this paper we consider the PBC techniques of Control by Interconnection (CbI) and Standard PBC. In CbI the controller is another PH system connected to the plant (through a power-preserving interconnection) to add up their energy functions, while in Standard PBC energy shaping is achieved via static state feedback. In spite of the conceptual appeal of formulating the control problem as the interaction of dynamical systems, the current version of CbI imposes a severe restriction on the plant dissipation structure that stymies its practical application. On the other hand, Standard PBC, which is usually derived from a uninspiring and non-intuitive ldquopassive output generationrdquo viewpoint, is one of the most successful controller design techniques. The main objectives of this paper are: (1) To extend the CbI method to make it more widely applicable-in particular, to overcome the aforementioned dissipation obstacle. (2) To show that various popular variants of Standard PBC can be derived proceeding from a unified perspective. (3) To establish the connections between CbI and Standard PBC proving that the latter is obtained restricting the former to a suitable subset-providing a nice geometric interpretation to Standard PBC-and comparing the size of the set of PH plants for which they are applicable.

Exponential Stabilization of a Wheeled Mobile Robot Via Discontinuous Control

In the present work the problem of exponential stabilization of the kinematic and dynamic model of a simple wheeled mobile robot is addressed and solved using a discontinuous, bounded, time invariant, state feedback control law. The properties of the closed-loop system are studied in detail and its performance in presence of model errors and noisy measurements are evaluated and discussed.

Model Reduction by Moment Matching for Linear and Nonlinear Systems

The model reduction problem for (single-input, single-output) linear and nonlinear systems is addressed using the notion of moment. A re-visitation of the linear theory allows to obtain novel results for linear systems and to develop a nonlinear enhancement of the notion of moment. This, in turn, is used to pose and solve the model reduction problem by moment matching for nonlinear systems, to develop a notion of frequency response for nonlinear systems, and to solve model reduction problems in the presence of constraints on the reduced model. Connections between the proposed results, projection methods, the covariance extension problem and interpolation theory are presented. Finally, the theory is illustrated by means of simple worked out examples and case studies.

Brief paper: High gain observers with updated gain and homogeneous correction terms

Exploiting dynamic scaling and homogeneity in the bi-limit, we develop a new class of high gain observers which incorporate a gain update law and nonlinear output error injection terms. A broader class of systems can be addressed and the observer gain is better fitted to the incremental rate of the nonlinearities. The expected improved performance is illustrated.

Conditions for stability of droop-controlled inverter-based microgrids

We consider the problem of stability analysis for droop-controlled inverter-based microgrids with meshed topologies. The inverter models include variable frequencies as well as voltage amplitudes. Conditions on the tuning gains and setpoints for frequency and voltage stability, together with desired active power sharing, are derived in the paper. First, we prove that for all practical choices of these parameters global boundedness of trajectories is ensured. Subsequently, assuming the microgrid is lossless, a port-Hamiltonian description is derived, from which sufficient conditions for stability are given. Finally, we propose for generic lossy microgrids a design criterion for the controller gains and setpoints such that a desired steady-state active power distribution is achieved. The analysis is validated via simulation on a microgrid based on the CIGRE (Conseil International des Grands Reseaux Electriques) benchmark medium voltage distribution network.