Andrea Alessandretti

On convergence and performance certification of a continuous-time economic model predictive control scheme with time-varying performance index

This paper addresses the design of convergence and performance certified sampled-data model predictive control (MPC) laws with a time-dependent economic performance index. More precisely, using a dissipativity property of the system, we provide a set of sufficient conditions that guarantee convergence of the closed-loop state trajectory to a, possibly time-varying, average economically optimal state trajectory. Moreover, the average performance of the closed-loop system is shown to be no worse than the one obtained by operating the system at the average economically optimal state trajectory. Constructive methods to design an appropriate terminal set and terminal cost that satisfy the proposed sufficient conditions are presented and illustrated with numerical examples.

An economic model predictive control scheme with terminal penalty for continuous-time systems

In this paper, convergence and performance properties of a sample-data continuous time model predictive control (MPC) scheme with economic performance index are developed. In particular, we provide sufficient conditions for convergence of the close loop state trajectory to a steady state and constructive methods to design a terminal set and a terminal cost to satisfy them. Further, considering an average performance index, sufficient conditions under which the system in closed loop with the MPC controller outperforms the system operated at the economically optimal steady state are derived for the case of convergent and non convergent behaviors. Two numerical examples are presented to illustrate the different design techniques.

A Model Predictive Control scheme with additional performance index for transient behavior

This paper presents a Model Predictive Control (MPC) scheme for nonlinear continuous time systems where an extra performance index, which is not a measure of the distance to the set point, is introduced to influence the transient behavior of the controlled system. The scheme is based on the following fact, proven in the paper: Given a stabilizing MPC controller, adding a function, integrable in the interval [t,+∞), to the stage cost does not change the asymptotic convergence property of the closed loop state trajectory. As a numerical example, this result is applied to solve a simple visual servo control problem where an MPC controller drives the state to the origin while penalizing weakly observable trajectories.

A Model predictive control scheme with ultimate bound for economic optimization

This paper presents a Model Predictive Control (MPC) scheme for nonlinear continuous-time systems where an economic stage cost, which is not a measure of the distance to a desired set point, is combined with a classic stabilizing stage cost. The associated control strategy leads to a closed-loop behavior that in a seamless way compromises between the convergence of the closed-loop state trajectory to a given steady-state and the minimization of the economic cost. More precisely, we derive a set of sufficient conditions under which the closed-loop state trajectory is ultimately bounded around the desired steady-state, with the size of the bound being proportional to the strength of the economic cost. Numerical results show the effectiveness of the proposed scheme on a simultaneous target estimation and tracking control problem.

VirtualArena: An object-oriented MATLAB toolkit for control system design and simulation

This paper presents an open-source object-oriented MATLAB toolkit for control system design and system simulation. The objective of the toolkit is to reduce the time required for the design and validation of a control architecture while at the same time increasing the reliability, modularity, and reusability of each of its components and fostering collaborative design and sharing of the developed components. To reduce the development time, a set of ready-to-use functions that are commonly required by control design processes is provided, such as automatic generation of Extended Kalman Filters, discretization, and many others. Moreover, we define a set of common interfaces to integrate the different standard components. The toolkit is introduced by means of a practical example, starting from the modeling of a planar Unmanned Aerial Vehicle, implementation of a two state-feedback controllers (one simple but nonlinear and another more complex using a Model Predictive Control approach), automatic generation of a state estimator, simulation, and remote network control over a Local Area Network.

A feedback motion strategy applied to a UAV to work as an autonomous relay node for maritime operations

One important aspect that needs to be carefully considered in maritime operations using unmanned robotic vehicles is the communication restrictions between the vehicles and the mission controller that arises mainly due to long distances and/or low power transmissions. This paper addresses the problem of maintaining a communication link between a command station and an Unmanned Aerial Vehicle (UAV) with limited communication range during maritime operations. The proposed scheme uses an additional UAV that acts as a relay for the communication between the command station and the UAV in mission and is actively driven to maintain a desired Quality-of-Service (QoS) level, defined in this paper. Exploiting this architecture, it is possible to plan a maritime operation for a robotic vehicle without the need of considering vehicle-to-command-station communication constraints that will be satisfied by the introduction of the extra autonomous relay-UAVs. To this end, we propose a feedback strategy that has the dual task of commanding and optimizing the execution of the relay UAV motion tasks and adapting the scheduler algorithm according to a desired QoS level. The performance of the proposed strategy is illustrated through computer simulations and preliminary experimental results.

Optimization based control for target estimation and tracking via highly observable trajectories

This paper proposes a Model Predictive Control (MPC) sche-me to solve the target estimation and tracking problem. The objective is to derive a feedback law that drives an autonomous robotic vehicle to follow a target vehicle using an on-line estimate of the target’s state. In this scenario, when the target is observed through a nonlinear observation model, e.g., bearing only or range only sensors, it is possible to show that solving the tracking problem independently from the estimation problem can lead to an unsatisfactory result where the follower-target system is driven by the controller through unobservable or weakly observable trajectories and, as result, the state of the target vehicle cannot be recovered or cannot be recovered with high accuracy leading to the failure of the control strategy. In this paper, we propose an optimization based scheme that embeds, in a seamless way, an index of observability in the design of the target tracking controller resulting in a closed loop behavior that balances the objective of target tracking with the competing objective of maintaining a good estimate of the state of the target. Numerical results are presented that illustrate this type of behavior.

A consensus algorithm for networks with process noise and quantization error

In this paper we address the problem of quantized consensus where process noise or external inputs corrupt the state of each agent at each iteration. We propose a quantized consensus algorithm with progressive quantization, where the quantization interval changes in length at each iteration by a pre-specified value. We derive conditions on the design parameters of the algorithm to guarantee ultimate boundedness of the deviation from the average of each agent. Moreover, we determine explicitly the bounds of the consensus error under the assumption that the process disturbances are ultimately bounded within known bounds. A numerical example of cooperative path-following of a network of single integrators illustrates the performance of the proposed algorithm.

A Sampled-Data Model Predictive Framework for Cooperative Path Following of Multiple Robotic Vehicles

We present a sampled-data model predictive control (MPC) framework for cooperative path following (CPF) of multiple, possibly heterogeneous, autonomous robotic vehicles. Under this framework, input and output constraints as well as meaningful optimization-based performance trade-offs can be conveniently addressed. Conditions under which the MPC-CPF problem can be solved with convergence guarantees are provided. An example illustrates the proposed approach.

An Input-to-State-Stability Approach to Economic Optimization in Model Predictive Control

This paper presents a model predictive control (MPC) scheme where a combination of a stabilizing stage cost and an economic stage cost is employed to allow the minimization of an economic performance index while still guaranteeing convergence toward a desired steady state. Input-to-state-stability with respect to the economic stage cost is provided. More precisely, for the case of an economic stage cost converging to zero, the economic optimization only affects the transient behavior of the closed-loop trajectories preserving the convergence to the desired steady state. Alternatively, if the economic stage cost is merely bounded, or convergent to a bound, the closed-loop state trajectory is ultimately bounded around the desired steady state with the size of the bound being monotonically increasing with the magnitude of the economic stage cost. The loosening of the closed-loop guarantees, i.e., moving from convergence to ultimate boundedness, gives space to the increase of economic performance. Numerical results illustrate the effectiveness of the proposed method on an energy efficient trajectory-tracking control problem of a marine robotic vehicle navigating in the presence of water currents.