Explicit Reference Governor for Continuous Time Nonlinear Systems Subject to Convex Constraints

This paper introduces a novel closed-form strategy that dynamically modifies the reference of a pre-compensated nonlinear system to ensure the satisfaction of a set of convex constraints. The main idea consists of translating constraints in the state space into constraints on the Lyapunov function and then modulating the reference velocity so as to limit the value of the Lyapunov function. The theory is introduced for general nonlinear systems subject to convex constraints. In the case of polyhedric constraints, an explicit solution is provided for the large and highly relevant class of nonlinear systems whose Lyapunov function is lower-bounded by a quadratic form. In view of improving performances, further specializations are provided for the relevant cases of linear systems and robotic manipulators.Comment: Submitted to: IEEE Transactions on Automatic Contro

Finite-Time Computation of Polyhedral Input-Saturated Output-Admissible Sets

The paper introduces a novel algorithm for computing the output admissible set of linear discrete-time systems subject to input saturation. The proposed method takes advantage of the piecewise-affine dynamics to propagate the output constraints within the non-saturated and saturated regions. The constraints are then shared between regions to ensure a proper transition from one region to another. The resulting algorithm generates a set that is proven to be polyhedral, safe, positively invariant, and finitely determined. Moreover, the set is also proven to be strictly larger than the maximal output admissible set that would be obtained by treating input saturation as a constraint.Comment: Submitted to IEEE Transactions on Automatic Contro

A Semismooth Predictor Corrector Method for Real-Time Constrained Parametric Optimization with Applications in Model Predictive Control

Real-time optimization problems are ubiquitous in control and estimation, and are typically parameterized by incoming measurement data and/or operator commands. This paper proposes solving parameterized constrained nonlinear programs using a semismooth predictor-corrector (SSPC) method. Nonlinear complementarity functions are used to reformulate the first order necessary conditions of the optimization problem into a parameterized non-smooth root-finding problem. Starting from an approximate solution, a semismooth Euler-Newton algorithm is proposed for tracking the trajectory of the primal-dual solution as the parameter varies over time. Active set changes are naturally handled by the SSPC method, which only requires the solution of linear systems of equations. The paper establishes conditions under which the solution trajectories of the root-finding problem are well behaved and provides sufficient conditions for ensuring boundedness of the tracking error. Numerical case studies featuring the application of the SSPC method to nonlinear model predictive control are reported and demonstrate the advantages of the proposed method

Advanced polymeric materials for applications in technical equipment for snow sports

The thesis is divided in three chapters, each one covering one topic. Initially, the thermo-mechanical and impact properties of materials used for back protectors have been analysed. Dynamical mechanical analysis (DMTA) has shown that materials used for soft-shell protectors present frequency-sensitive properties. Furthermore, through impact tests, the shock absorbing characteristics of the materials have been investigated proving the differences between soft and hard-shell protectors; moreover it has been demonstrated that the materials used for soft-shell protectors maintain their protective properties after multi-impacts. The second chapter covers the effect of the visco-elastic properties of the thermoplastic polymers on the flexural and rebound behaviours of ski boots. DMTA analysis on the materials and flexural and rebound testing on the boots have been performed. A comparison of the results highlighted a correlation between the visco-elastic properties and the flexural and rebound behaviour of ski boots. The same experimental methods have been used to investigate the influence of the design on the flexural and rebound behaviours. Finally in the third chapter the thermoplastic materials employed for the construction of ski boots soles have been characterized in terms of chemical composition, hardness, crystallinity, surface roughness and coefficient of friction (COF). The results showed a relation between material hardness and grip, in particular softer materials provide more grip with respect to harder materials. On the contrary, the surface roughness has a negative effect on friction because of the decrease in contact area. The measure of grip on inclined wet surfaces showed again a relation between hardness and grip. The performance ranking of the different materials has been the same for the COF and for the slip angle tests, indicating that COF can be used as a parameter for the choice of the optimal material to be used for the soles of ski boots

How to solve Quantum Optimal Control Problems using Projection Operator-based Newton Steps

The Quantum PRojection Operator-based Newton method for Trajectory Optimization, a.k.a. Q-PRONTO, is a numerical method for solving quantum optimal control problems. This paper significantly improves prior versions of the quantum projection operator by introducing a regulator that stabilizes the solution estimate at every iteration. This modification is shown to not only improve the convergence rate of the algorithm, but also steer the solver towards better local minima compared to the un-regulated case. Numerical examples showcase Q-PRONTO can be used to solve multi-input quantum optimal control problems featuring time-varying costs and undesirable populations that ought to be avoided during the transient.Comment: 10 pages, 9 figure

Attitude Trajectory Optimization and Momentum Conservation with Control Moment Gyroscopes

In this work, we develop a numerically tractable trajectory optimization problem for rest-to-rest attitude transfers with CMG-driven spacecraft. First, we adapt a specialized dynamical model which avoids many of the numerical challenges (singularities) introduced by common dynamical approximations. To formulate and solve our specialized trajectory optimization problem, we design a locally stabilizing Linear Quadratic (LQ) regulator on the system's configuration manifold then lift it into the ambient state space to produce suitable terminal and running LQ cost functionals. Finally, we examine the performance benefits and drawbacks of solutions to this optimization problem via the PRONTO solver and find significant improvements in maneuver time, terminal state accuracy, and total control effort. This analysis also highlights a critical shortcoming for objective functions which penalize only the norm of the control input rather than electrical power usage.Comment: 8 pages, 6 figures, IFAC 2023 conference submissio