Simone Baldi

A "plug and play" computationally efficient approach for control design of large-scale nonlinear systems using cosimulation: a combination of two "ingredients"

This article describes a computationally efficient simulation-based control design approach that has the capability of handling optimization problems arising from large-scale nonlinear systems, with fast convergence properties and low computational requirements. The purpose of this article is to describe the main features of the PCAO algorithm, analyze its convergence and stability properties, and demonstrate its efficiency using simulations of two large-scale, real-life systems (a traffic network and an energy-efficient building) for which conventional optimization techniques fail to provide an efficient simulation-based control design.

A “plug-n-play” computationally efficient approach for control design of large-scale nonlinear systems using co-simulation

Recently, there has been a growing interest towards simulation-based control design (co-simulation), where the controller utilizes an optimizer to minimize or maximize an objective function (system performance) whose evaluation involves simulation of the system to be controlled. However, existing simulation-based approaches are not able to handle in a computationally efficient way large-scale optimization problems involving hundreds or thousands of states and parameters. In this paper, we propose and analyze a new simulation-based control design approach, employing an adaptive optimization algorithm capable of efficiently handle large-scale control problems. The convergence properties of the proposed algorithm are established. Simulation results exhibit efficiency of the proposed approach when applied to large-scale problems. The simulation results employ two large-scale real-life systems for which conventional popular optimization techniques totally fail to provide an efficient simulation-based control design.

Multiple Model Adaptive Mixing Control: The Discrete-Time Case

Most of the work in multiple model adaptive control with various forms of switching focused on continuous-time systems. The purpose of this technical note is to extend the results of one approach, the adaptive mixing control (AMC), to discrete-time systems. Further, the technical note solves the tracking problem which has not been addressed in most schemes of this class. Stability and robustness properties of the AMC scheme for discrete-time systems are analyzed. It is shown that in the ideal case, when no disturbances or unmodeled dynamics are present, the tracking error converges to zero. In the non ideal case, the mean-square tracking error is of the order of magnitude of the modeling error provided the unmodeled dynamics satisfy a norm-bound condition. While these robustness results are conceptually similar to those of traditional robust adaptive control, the proposed scheme does not suffer from the drawback of stabilizability of the estimated plant and in addition performs much better in simulation studies. Furthermore, it allows well developed results from robust control to be incorporated in the design.

Convex Design Control for Practical Nonlinear Systems

This paper describes a new control scheme for approximately optimal control (AOC) of nonlinear systems, convex control design (ConvCD). The key idea of ConvCD is to transform the approximate optimal control problem into a convex semi-definite programming (SDP) problem. Contrary to the majority of existing AOC designs where the problem that is addressed is to provide a control design which approximates the performance of the optimal controller by increasing the “controller complexity,” the proposed approach addresses a different problem: given a controller of “fixed complexity” it provides a control design that renders the controller as close to the optimal as possible and, moreover, the resulted closed-loop system stable. Two numerical examples are used to show the effectiveness of the method.

Adaptive Asymptotic Tracking Control of Uncertain Time-Driven Switched Linear Systems

This technical note establishes a novel result for adaptive asymptotic tracking control of uncertain switched linear systems. The result exploits a recently proposed stability condition for switched systems. In particular, a time-varying positive definite Lyapunov function is used to develop a novel piecewise continuous model-reference adaptive law and a dwell-time switching law. In contrast with previous research, where asymptotic tracking was possible only in the presence of a common Lyapunov function for the reference models, in this work asymptotic tracking is shown in a more general setting. Additionally, in the presence of persistence of excitation, the controller parameter estimation errors will converge to zero asymptotically. The main contribution of this work consists in establishing a symmetry between adaptive control of classical non-switched linear systems and adaptive control of switched linear systems. A practical example with an electro-hydraulic system is adopted to illustrate the results.

Automatic Tuning of the Internal Position Control of an Adaptive Secondary Mirror

One of the key components of an Adaptive Optics system is the deformable mirror. This mirror can correct the atmospheric turbulence effects by changing its shape. In the last years Adaptive Secondary Mirrors (ASM) have been developed and the Large Binocular Telescope (LBT) will be soon equipped with two ASMs. Each LBT ASM unit has 672 voice-coil force actuators to change the shape of the mirror shell. Because the actuators apply force, an internal position control is required. The LBT ASM internal control uses a local feedback of position and velocity, then the control law for each actuator has two characteristic parameters which define the closed-loop shell dynamics. In this paper, an analysis of the dynamical behaviour of the ASM under the proposed control law is provided. Then an algorithm is suggested that, based on a simplified model of the shell dynamics, tunes the controller parameters by means of an automatic procedure, as a replacement for a manual procedure based on the operator skill.

An Adaptive Switched Control Approach to Heterogeneous Platooning With Intervehicle Communication Losses

The advances in distributed intervehicle communication networks have stimulated a fruitful line of research in cooperative adaptive cruise control (CACC). In CACC, individual vehicles, grouped into platoons, must automatically adjust their own speed using on-board sensors and communication with the preceding vehicle so as to maintain a safe intervehicle distance. However, a crucial limitation of the state of the art of this control scheme is that the string stability of the platoon can be proven only when the vehicles in the platoon have identical driveline dynamics and perfect engine performance (homogeneous platoon), and possibly an ideal communication channel. This paper proposes a novel CACC strategy that overcomes the homogeneity assumption and that is able to adapt its action and achieve string stability even for uncertain heterogeneous platoons. Furthermore, in order to handle the inevitable communication losses, we formulate an extended average dwell-time framework and design an adaptive switched control strategy, which activates an augmented CACC or an augmented adaptive cruise control strategy depending on communication reliability. Stability is proven analytically and simulations are conducted to validate the theoretical analysis.

Simulation-based synthesis for approximately optimal urban traffic light management

Suitable control measures and strategies must be taken to counteract the reduced throughput and the degradation of the network infrastructure caused by traffic congestion in urban networks. This paper studies and analyzes the performance of an adaptive traffic-responsive strategy that manages the traffic light parameters (the cycle time and the split time) in an urban network to reduce traffic congestion. The proposed traffic-responsive strategy adopts a nearly-optimal control formulation: first, an (approximate) solution of the HJB is parametrized via an appropriate Lyapunov positive definite matrix; then, the solution is updated via a procedure that generates candidate control strategies and selects at each iteration the best one based on the estimation of close-to-optimality and the information coming from the simulation model of the network (simulation-based design). Simulation results obtained using an AIMSUN model of the traffic network of Chania, Greece, an urban traffic network containing many varieties of junction staging, demonstrate the efficiency of the proposed approach.

Evaluation of identifier based and & non-identifier based adaptive supervisory & control using a benchmark example

Several classes of identifier and non-identifier based adaptive control schemes using a supervisory switching logic have been proposed in the literature. These schemes are based on different assumptions and claim to guarantee certain stability and performance properties. The purpose of this paper is to clarify what each algorithm guarantess in theory and how it performs in simulations. The identifier based schemes: Robust Multiple Model Adaptive Control (RMMAC) and Adaptive Mixing Control (AMC) and the non-identifier based schemes: Unfalsified Adaptive Switching Control (UASC) and Multi-model Unfalsified Adaptive Switching Control (MUASC). For each scheme we present the basic features of the algorithm and state the stability and performance guaranteed in theory. The benchmark example of [1] is used to test the stability and performance properties of the schemes considered using extensive simulations. Our results show that the identifier based schemes require some knowledge about the plant whereas the non identifier based do not. The identifier based schemes however typically perform better than non-identifier based schemes when all the plant assumptions are satisfied, and can guarantee, from a theory viewpoint, at least for the AMC scheme, transient and asymptotic performance. The main positive feature the UASC and MUASC schemes is that, even in the absence of any prior information on the uncertain plant, they can select in finite time a final controller yielding, a finite affine gain from the reference to the data, under the minimal conceivable requirement, viz. the existence of a stabilizing candidate controller in the candidate controller set.

Stability margins in adaptive mixing control via a Lyapunov-based switching criterion

In all classes of linear adaptive control that involve switching or not there is no guarantee that after the switching stops or the adaptation is switched off the resulting closed loop linear time invariant system is stable let alone have a certain stability margin unless the persistence of excitation condition is satisfied. It will be of great practical importance if in the case of switching adaptive control we can converge to a controller that is stabilizing with certain stability margins. In this paper, a switching logic ensuring Lyapunov stability is proposed inside the framework of adaptive mixing control (AMC). The switching logic uses a Lyapunov based criterion to assess which controller should be put in the loop. The resulting scheme guarantees that the final switched-on controller satisfies a Lyapunov inequality implying a prescribed stability margin. A numerical example is used to show the effectiveness of the method.