A Unified Framework for the H∞ Mixed-Sensitivity Design of Fixed Structure Controllers through Putinar Positivstellensatz

In this paper, we present a novel technique to design fixed structure controllers, for both continuous-time and discrete-time systems, through an H∞ mixed sensitivity approach. We first define the feasible controller parameter set, which is the set of the controller parameters that guarantee robust stability of the closed-loop system and the achievement of the nominal performance requirements. Then, thanks to Putinar positivstellensatz, we compute a convex relaxation of the original feasible controller parameter set and we formulate the original H∞ controller design problem as the non-emptiness test of a set defined by sum-of-squares polynomials. Two numerical simulations and one experimental example show the effectiveness of the proposed approach

The Educational Benefit of a Remote Automatic Control Laboratory. A Win-Win Collaboration between Asia and Europe

This project aims to implement a Remote European Asian Lab, an Automatic Control remote laboratory, in the joint academic cooperation framework between two universities located in Europe and Central Asia. Emphasis is given to the inclusive solution of a shared teaching facility and its learning achievements in a bachelor course (Uzbekistan) and a master course (Italy) to foresee a better education quality. The different cultural and social contexts allow (a) the evaluation of the effect obtained by introducing a remote laboratory experience in a course entirely theoretical, and (b) the shift from a physical laboratories experience to a remote one. Students are first introduced to this laboratory by the lecturer in dedicated classes. Then students can independently access it 24/7 by simply booking a specific station for a time slot. From the analysis comes out that remote laboratory experiences positively impact learning achievements. The benefits of the remote environment are perfectly comparable with those obtained from physical laboratory activities

Whole-Body Trajectory Optimization for Robot Multimodal Locomotion

The general problem of planning feasible trajec-tories for multimodal robots is still an open challenge. This paper presents a whole-body trajectory optimisation approach that addresses this challenge by combining methods and tools developed for aerial and legged robots. First, robot models that enable the presented whole-body trajectory optimisation framework are presented. The key model is the so-called robot centroidal momentum, the dynamics of which is directly related to the models of the robot actuation for aerial and terrestrial locomotion. Then, the paper presents how these models can be employed in an optimal control problem to generate either terrestrial or aerial locomotion trajectories with a unified approach. The optimisation problem considers robot kinematics, momentum, thrust forces and their bounds. The overall approach is validated using the multimodal robot iRonCub, a flying humanoid robot that expresses a degree of terrestrial and aerial locomotion. To solve the associated optimal trajectory generation problem, we employ ADAM, a custom-made open-source library that implements a collection of algorithms for calculating rigid- body dynamics using CasADi

A Unified Framework for the H∞ Mixed-Sensitivity Design of Fixed Structure Controllers through Putinar Positivstellensatz

In this paper, we present a novel technique to design fixed structure controllers, for both continuous-time and discrete-time systems, through an H∞ mixed sensitivity approach. We first define the feasible controller parameter set, which is the set of the controller parameters that guarantee robust stability of the closed-loop system and the achievement of the nominal performance requirements. Then, thanks to Putinar positivstellensatz, we compute a convex relaxation of the original feasible controller parameter set and we formulate the original H∞ controller design problem as the non-emptiness test of a set defined by sum-of-squares polynomials. Two numerical simulations and one experimental example show the effectiveness of the proposed approach

Nonlinear Model Predictive ControlFast Algorithms and Implementation

The problem of an efficient implementation of a Model Predictive Control (MPC) algorithm is addressed in this dissertation. The nominal problem formulation for the MPC control law involves the solution, for each sample time, to an optimization problem that is, in general, nonlinear and hard to be solved. The sample time must be greater than the time required to solve the optimization problem and, as a consequence, MPC cannot be directly applied to system with a fast dynamics. To overcome this problem, two possible approaches are proposed here: a set-membership (SM) based technique and a approximation of the optimization solver. The proposed SM based technique, substantially, allows to avoid solving the optimization problem on-line at each sample time. The control move is computed by means of a set of pre-computed solutions to the optimization problem for a given number of different system state values. This approach is potentially applicable to every kind of system, with the disadvantage to require a large amount of memory needed to store the data for the approximation. By focusing on the case of the linear MPC, other approximations can be used to obtain a fast implementation of a MPC controller with no pre-computed solutions. A modified interior-point algorithm which guarantee execution time in the order of a millisecond is described in this thesis. The effectiveness of the proposed techniques is shown through examples from real world applications. The examples were chosen from the set of such applications whose properties that prevent the applicability of the nominal predictive controller. The obtained simulations results shown the effectiveness of the proposed approximation technique

MIMO linear systems identification in the presence of bounded noise

In this paper we consider the problem of set-membership identification of multiple-inputs multiple-outputs (MIMO) linear models when both input and output measurements are affected by bounded additive noise. First a general formulation is proposed which allows the user to take into account possible a-priori information about the structure of the MIMO model to be identified. Then, the problem is formulated in terms of a suitable polynomial optimization problem, which is solved by means of a convex relaxation approach. A simulation example is presented in order to show the effectiveness of the proposed approac