Claudio De Persis

Switched nonlinear systems with state-dependent dwell-time

The asymptotic convergence of a switched nonlinear system in the presence of disturbances is studied. The system switches among a family of integral input-to-state stable systems. The time between two consecutive switchings is not less than a value τD. This dwell-time τD is allowed to take different values according to a function whose argument is the state of the system at the switching times. We propose a dwell-time function which depends on the comparison functions which characterize the integral input-to-state stability property and guarantees the state of the switched system to converge to zero under the action of disturbances with “bounded energy”. The main feature of the analysis is that it does not rely on the property for the switching to stop in finite time. The two important cases of locally exponentially stable and feedforward systems are analyzed in detail.

Stabilizability by state feedback implies stabilizability by encoded state feedback

Abstract Encoded state feedback is a term which refers to the situation in which the state feedback signal is sampled every T units of time and converted (encoded) into a binary representation. In this note stabilization of nonlinear systems by encoded state feedback is studied. It is shown that any nonlinear control system which can be globally asymptotically stabilized by “standard” (i.e. with no encoding) state feedback can also be globally asymptotically stabilized by encoded state feedback, provided that the number of bits used to encode the samples is not less than an explicitly determined lower bound. By means of this bound, we are able to establish a direct relationship between the size of the expected region of attraction and the data rate, under the stabilizability assumption only, a result which—to the best of our knowledge—does not have any precedent in the literature.

Discontinuous stabilization of nonlinear systems: Quantized and switching controls

In this paper we consider the classical problem of stabilizing nonlinear systems in the case the control laws take values in a discrete set. First, we present a robust control approach to the problem. Then, we focus on the class of dissipative systems and rephrase classical results available for this class taking into account the constraint on the control values. In this setting, feedback laws are necessarily discontinuous and solutions of the implemented system must be considered in some generalized sense. The relations with the problems of quantized and switching control are discussed

Robust stabilization of nonlinear systems by quantized and ternary control

Results on the problem of stabilizing a nonlinear continuous-time minimum-phase system by a finite number of control or measurement values are presented. The basic tool is a discontinuous version of the so-called semi-global backstepping lemma. We derive robust practical stabilizability results by quantized and ternary controllers and apply them to some control problems. Estimates on the required bandwidth are also provided.

Supervisory control with state-dependent dwell-time logic and constraints

The paper deals with the supervisory control of a nonlinear uncertain system in which the switching is directed by the recently introduced state-dependent dwell-time switching logic. The proposed supervisory control architecture is shown to regulate to zero the state of the system without requiring the switching to stop in finite time. A significant class of systems to which the control architecture can be applied is the class of linear systems with input saturation.

Coordination of Passive Systems under Quantized Measurements

In this paper we investigate a passivity approach to collective coordination and synchronization problems in the presence of quantized measurements and show that coordination tasks can be achieved in a practical sense for a large class of passive systems.

On a small-gain approach to distributed event-triggered control

Abstract In this paper the problem of stabilizing large-scale systems by distributed controllers, where the controllers exchange information via a shared limited communication medium is addressed. An event-triggered sampling scheme is proposed, in which each system decides when to transmit new information across the network based on the crossing of some error threshold. Stability of the interconnected large-scale system is inferred by applying a generalized small-gain theorem.

Stability of quantized time-delay nonlinear systems: a Lyapunov–Krasowskii-functional approach

Lyapunov–Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of constant delays in the input. The quantized control law is implemented via hysteresis to avoid chattering. Under appropriate conditions, our analysis applies to stabilizable nonlinear systems for any value of the quantization density. The resulting quantized feedback is parametrized with respect to the quantization density. Moreover, the maximal allowable delay tolerated by the system is characterized as a function of the quantization density.

Quantization effects on synchronized motion of teams of mobile agents with second-order dynamics

Abstract For a team of mobile agents governed by second-order dynamics, this paper studies how different quantizers affect the performances of consensus-type schemes to achieve synchronized collective motion. It is shown that when different types of quantizers are used for the exchange of relative position and velocity information between neighboring agents, different collective behaviors appear. Under the chosen logarithmic quantizers and with symmetric neighbor relationships, we prove that the agents’ velocities and positions get synchronized asymptotically. We show that under the chosen symmetric uniform quantizers and with symmetric neighbor relationships, the agents’ velocities converge to the same value asymptotically while the differences of their positions converge to a bounded set. We also show that when the uniform quantizers are not symmetric, the agents’ velocities may grow unboundedly. Through simulations we present richer undesirable system behaviors when different logarithmic and uniform quantizers are used. Such different quantization effects underscore the necessity for a careful selection of quantization strategies, especially for multi-agent systems with higher-order agent dynamics.

Input-to-state stable finite horizon MPC for neutrally stable linear discrete-time systems with input constraints

Abstract MPC or model predictive control is representative of control methods which are able to handle inequality constraints. Closed-loop stability can therefore be ensured only locally in the presence of constraints of this type. However, if the system is neutrally stable, and if the constraints are imposed only on the input, global asymptotic stability can be obtained; until recently, use of infinite horizons was thought to be inevitable in this case. A globally stabilizing finite-horizon MPC has lately been suggested for neutrally stable continuous-time systems using a non-quadratic terminal cost which consists of cubic as well as quadratic functions of the state. The idea originates from the so-called small gain control, where the global stability is proven using a non-quadratic Lyapunov function. The newly developed finite-horizon MPC employs the same form of Lyapunov function as the terminal cost, thereby leading to global asymptotic stability. A discrete-time version of this finite-horizon MPC is presented here. Furthermore, it is proved that the closed-loop system resulting from the proposed MPC is ISS (Input-to-State Stable), provided that the external disturbance is sufficiently small. The proposed MPC algorithm is also coded using an SQP (Sequential Quadratic Programming) algorithm, and simulation results are given to show the effectiveness of the method.