Bruno Picasso

On the Stabilization of Linear Systems Under Assigned I/O Quantization

This paper is concerned with the stabilization of discrete-time linear systems with quantization of the input and output spaces, i.e., when available values of inputs and outputs are discrete. Unlike most of the existing literature, we assume that how the input and output spaces are quantized is a datum of the problem, rather than a degree of freedom in design. Our focus is hence on the existence and synthesis of symbolic feedback controllers, mapping output words into the input alphabet, to steer a quantized I/O system to within small invariant neighborhoods of the equilibrium starting from large attraction basins. We provide a detailed analysis of the practical stabilizability of systems in terms of the size of hypercubes bounding the initial conditions, the state transient, and the steady-state evolution. We also provide an explicit construction of a practically stabilizing controller for the quantized I/O case.

An MPC approach to the design of two-layer hierarchical control systems

A methodology for the design of two-layer hierarchical control systems is presented. The high layer corresponds to a system with slow dynamics, whose control inputs must be provided by subsystems with faster dynamics placed at the low layer. Model Predictive Control laws are synthesized for both layers and overall convergence properties are established. The use of different control configurations is also considered by allowing the switching on/off of the subsystems at the low layer. A simulation example is reported to witness the potentialities of the proposed solution.

Almost Sure Stabilization of Uncertain Continuous-Time Markov Jump Linear Systems

This work deals with the robust almost sure (AS) stabilization problem for continuous-time Markov jump linear systems (MJLS). Norm-bounded uncertainties affecting the system state and input matrices are considered. A deterministically testable sufficient condition for robust AS stability is provided which relies on a bound on the 2-norm of the system transition matrix. Such a condition can be profitably employed also to design a robust feedback stabilization strategy. Such feedback design is based on a formulation of the sufficient condition for robust AS stability in terms of an equivalent LMI problem.

Construction of invariant and attractive sets for quantized-input linear systems

In this paper, the problem of the stabilization of a discrete-time linear system subject to a fixed and uniformly quantized control set is considered. It is well known that, working with quantized inputs, the states of the system (except for a negligible set of initial conditions) cannot reach asymptotically the equilibrium point. Our aim is then to find an invariant and attractive neighborhood of the equilibrium and provide with a controller which steers the system into it. We construct a continuous and increasing family of invariant sets including one which is, in a specific sense, minimal. The invariance and attractivity properties of such sets are revised in the finite control set case: we propose a family of controllers taking on a finite number of values and ensuring the system convergence to the minimal invariant set. Some consequences of our technique axe underlined with particular regard to the usage of model predictive control tools. In the last section an example which shows the effectiveness of our results is presented.

A Smartphone-in-the-Loop Active State-of-Charge Manager for Electric Vehicles

Environmental concerns and the steadily decreasing oil supplies have promoted a significant interest in electric vehicles as a solution for the mobility of the near future, especially in urban environments. The correct handling of the energy behavior on board is one of the most critical problems to be addressed, particularly in urban driving scenarios where the speed profiles - even on fixed routes - are affected by significant unknown disturbances. To address this issue, this paper proposes a novel, spatially distributed and hierarchical control architecture that is capable of regulating the battery state of charge by imposing a desired discharge rate. The effectiveness of the overall control system is assessed by experimental results obtained on a prototype of a light-electric two-wheeled vehicle.

Robust Stability Analysis of Nonlinear Discrete-Time Systems With Application to MPC

The regional Input-to-State Stability of nonlinear, possibly discontinuous, discrete-time systems is studied under the assumption that the equilibrium of the corresponding nominal model is asymptotically stable. The obtained results are used for the synthesis of a nominal Model Predictive Control law ensuring inherent robustness. A numerical example is reported that witnesses the effectiveness of the approach.

Receding Horizon Control of LTI systems with quantized inputs

Abstract This paper deals with the stabilization problem for a particular class of hybrid systems, namely discrete-time linear systems subject to a uniform (a priori fixed) quantization of the control set. Results of our previous work on the subject provided a description of minimal (in a specific sense) invariant sets that could be rendered maximally attractive under any quantized feedback strategy. In this paper, we consider the design of stabilizing laws that optimize a given cost index on the state and input evolution on a finite, receding horizon. Application of Model Predictive Control techniques for the solution of similar hybrid control problems through Mixed Logical Dynamical reformulations can provide a stabilizing control law, provided that the feasibility hypotheses are met. In this paper, we discuss precisely what are the shortest horizon length and the minimal invariant terminal set for which it can be guaranteed a stabilizing MPC scheme. The simulation of the application of the control scheme to a practical quantized control problem is finally reported.

Stabilization of LTI systems with quantized state - quantized input static feedback

This paper is concerned with the stabilizability problem for discrete-time linear systems subject to a uniform quantization of the control set and to a regular state quantization, both fixed a priori. As it is well known, for quantized systems only weak (practical) stability properties can be achieved. Therefore, we focus on the existence and construction of quantized controllers capable of steering a system to within invariant neighborhoods of the equilibrium. We first consider uniformly quantized, unbounded input sets for which an increasing family of invariant sets is constructed and quantized controllers realizing invariance are characterized. The family contains a minimal set depending only on the quantization resolution. The analysis is then extended to cases where the control set is bounded: for any given state-space set of the family above, the minimal diameter of the control set which ensures its invariance is found. The finite control set so determined also guarantees that all the states of the set can be controlled in finite time to within the familys minimal set. It is noteworthy that the same property holds for systems without state quantization: hence, to ensure invariance and attractivity properties, the necessary control set diameter is invariant with state quantization; yet the minimal invariant set is larger. An example is finally reported to illustrate the above results.

Control-oriented energy-profiling and modelling of urban electric vehicles

Electric vehicles (EVs) are attracting more and more attention as a means to reach the desired reduction in transport-induced greenhouse emissions. To ensure an effective energetic management of these vehicles, especially in urban areas, dedicated control strategies are needed that correctly deal with the constraints related to the battery usage while preserving a good driving feeling. A preliminary step for the design of an effective controller is to get a reliable model of the vehicle dynamics of interest and thorough understanding of the energy flows in the vehicle itself. To this end, this paper proposes a systematic way to perform an energy-profiling of urban EVs and addresses the modelling and identification steps needed to achieve a control-oriented description of the vehicle longitudinal dynamics. Validation results are provided from data measured on a light electric two-wheeled vehicle.

Stabilization of discrete-time quantized linear systems: An H ∞ /l 1 approach

A generalized small-gain theorem, suitable for the analysis of practical stability, is proved in the framework of l₁ control. The result is combined with a practical stabilization technique based on a generalized small-gain theorem in H_∞. The resulting mixed H_∞/l₁ approach allows us to provide systematic tools for the control synthesis and the closed loop analysis in the practical stabilization of linear systems under assigned input quantization. A numerical example is reported.