Alessandro Borri

Integrated Design of Symbolic Controllers for Nonlinear Systems

Symbolic models of continuous and hybrid systems have been studied for a long time, because they provide a formal approach to solve control problems where software and hardware interact with the physical world. While being powerful, this approach often encounters some limitations in concrete applications, because of the large size of the symbolic models needed to be constructed. Inspired by on-the-fly techniques for verification and control of finite state machines, in this note we propose an algorithm that integrates the construction of the symbolic models with the design of the symbolic controllers. Computational complexity of the proposed algorithm is discussed and an illustrative example is included.

Adaptive integrated vehicle control using active front steering and rear torque vectoring

This work studies the combination of active front steering with rear torque vectoring actuators in an integrated controller to guarantee vehicle stability/trajectory tracking. Adaptive feedback technique has been used to design the controller. The feedback linearization is applied to cancel the nonlinearities in the input-output dynamics, leading to closed-loop dynamics diffeomorphic to a linear system. Parameter adaptation then is used to robustify the exact cancellation of the nonlinear terms. Some first results are here obtained, showing improved tracking performance when important parameters, like mass, inertia or tire stiffness, are affected by relevant estimation errors.

Randomized sampling for large zero-sum games

This paper addresses the solution of large zero-sum matrix games using randomized methods. We formalize a procedure, termed as the sampled security policy (SSP) algorithm, by which a player can compute policies that, with a high confidence, are security policies against an adversary using randomized methods to explore the possible outcomes of the game. The SSP algorithm essentially consists of solving a stochastically sampled subgame that is much smaller than the original game. We also propose a randomized algorithm, termed as the sampled security value (SSV) algorithm, which computes a high-confidence security-level (i.e., worst-case outcome) for a given policy, which may or may not have been obtained using the SSP algorithm. For both the SSP and the SSV algorithms we provide results to determine how many samples are needed to guarantee a desired level of confidence. We start by providing results when the two players sample policies with the same distribution and subsequently extend these results to the case of mismatched distributions. We demonstrate the usefulness of these results in a hide-and-seek game that exhibits exponential complexity.

Decentralized symbolic control of interconnected systems with application to vehicle platooning

This work aims at extending some concepts of symbolic control design to decentralized control structures, with an approximate simulation approach. Symbolic models and controllers are based on abstractions of continuous dynamics where one symbol corresponds to an aggregate of continuous states. We consider a serial interconnection of continuous nonlinear systems and we address the decentralized design of local controllers to accomplish a given specification on the overall system. The results are applied to a vehicle platooning problem, where we jointly fulfill a safety constraint (collision avoidance) and reduce the fuel consumption.

Integrated symbolic design of unstable nonlinear Networked Control Systems

The research area of Networked Control Systems (NCS) has been the topic of intensive study in the last decade. In this paper we give a contribution to this research line by addressing symbolic control design of (possibly unstable) nonlinear NCS with specifications expressed in terms of automata. We first derive symbolic models that are shown to approximate the given NCS in the sense of (alternating) approximate simulation. We then address symbolic control design with specifications expressed in terms of automata. We finally derive efficient algorithms for the synthesis of the proposed symbolic controllers that cope with the inherent computational complexity of the problem at hand.

Symbolic models for nonlinear control systems affected by disturbances

In the last few years, there has been a growing interest in the use of symbolic models for the formal verification and control design of purely continuous or hybrid systems. Symbolic models are abstract descriptions of continuous systems where one symbol corresponds to an ‘aggregate’ of continuous states. In this article, we face the problem of deriving symbolic models for nonlinear control systems affected by disturbances. The main contribution of this article is in proposing symbolic models that can be effectively constructed and that approximate nonlinear control systems affected by disturbances in the sense of alternating approximate bisimulation.

Active Control of Vehicle Attitude with Roll Dynamics

Abstract In this work an integrated attitude control of a vehicle is designed. The actuators considered are the active front steering, the rear torque vectoring, and the semi–active suspensions. We design also an algorithm for the saturation management. The resulting controller is hybrid. In nominal conditions, when saturation conditions do not occur, a feedback guarantees exponential tracking of the reference trajectories. In critical conditions, a hybrid feedback law assigns higher priority to some states to improve the tracking. It is shown that the saturation management improves the controller performance. Some simulations results are provided, showing the performance of the proposed controller.

Smart management of actuator saturation in integrated vehicle control

Integrated control design to guarantee vehicle stability is one of the main topics in vehicle control. Actuators saturation is a main concern when dealing with this issue. In this work, we propose a fully integrated control by means of three actuators: Active Front Steering (AFS), Rear Torque Vectoring (RTV) and Semi-Active Suspensions (SAS). A feedback controller is used to ensure, in absence of input saturation, the exponential tracking of the reference trajectories. On top of that, a smart saturation management scheme detects when the actuators approach the occurrence of saturation, and determines a policy to avoid actuator saturations. The performance of the resulting control strategy, that is hybrid in general, is tested in simulation and compared with some classical solutions.

Hide-and-Seek with Directional Sensing*

Abstract We consider a game played between a hider, who hides a static object in one of several possible positions in a bounded planar region, and a searcher, who wishes to reach the object by querying sensors placed in the plane. The searcher is a mobile agent, and whenever it physically visits a sensor, the sensor returns a random direction, corresponding to a half-plane in which the hidden object is located. We first present a novel search heuristic and characterize bounds on the expected distance covered before reaching the object. Next, we model this game as a large-dimensional zero-sum dynamic game and we apply a recently introduced randomized sampling technique that provides a probabilistic level of security to the hider. We observe that, when the randomized sampling approach is only allowed to select a very small number of samples, the cost of the heuristic is comparable to the security level provided by the randomized procedure. However, as we allow the number of samples to increase, the randomized procedure provides a higher probabilistic security level.

Some results on the structural properties and the solution of the Chemical Master Equation

The Chemical Master Equation (CME) is a well known tool for studying (bio)chemical processes involving few copies of the species involved, because it is a framework able to capture random behaviors that are neglected by deterministic approaches based on the concentration dynamics. In this work, we investigate some structural properties of CMEs and their solutions, with a particular focus on the efficient computation of the stationary distribution. We introduce a generalized notion of one-step process, which results in a sparse dynamical matrix describing the collection of the scalar CMEs, also showing a recursive block-tridiagonal structure. Further properties are inferred by means of a graph-theoretical interpretation of the reaction network. Examples are included to illustrate the notions and to show the effectiveness of the proposed approach.