Publications (49)
Incremental Gauss-Newton Descent for Machine Learning
Mikalai Korbit, Mario Zanon
Stochastic gradient updates are widely used for their efficiency and scalability, but their effective step sizes can depend strongly on feature scaling and local model sensitivity.…
On Two-Player Scalar Discrete-Time Linear Quadratic Games
Chiara Cavalagli, Alberto Bemporad, Mario Zanon
For the characterization of Feedback Nash Equilibria (FNE) in linear quadratic games, this paper provides a detailed analysis of the discrete-time discounted coupled best-response…
Optimal Scheduling of Downlink Communication for a Multi-Agent System with a Central Observation Post
Mario Zanon, Themistoklis Charalambous, Henk Wymeersch +1
In this paper, we consider a set of agents, which may receive an observation of their state by a central observa- tion post via a shared wireless network. The aim of this work is t…
Data-driven synthesis of Robust Invariant Sets and Controllers
Sampath Kumar Mulagaleti, Alberto Bemporad, Mario Zanon
This paper presents a method to identify an uncertain linear time-invariant (LTI) prediction model for tube-based Robust Model Predictive Control (RMPC). The uncertain model is det…
Safe Reinforcement Learning via Projection on a Safe Set: How to Achieve Optimality?
Sebastien Gros, Mario Zanon, Alberto Bemporad
For all its successes, Reinforcement Learning (RL) still struggles to deliver formal guarantees on the closed-loop behavior of the learned policy. Among other things, guaranteeing…
Rethinking Strict Dissipativity for Economic MPC
Mario Zanon
Stability of economic model predictive control can be proven under the assumption that a strict dissipativity condition holds. This assumption has a clear interpretation in terms o…
Stabilization of Strictly Pre-Dissipative Receding Horizon Linear Quadratic Control by Terminal Costs
Mario Zanon, Lars Grüne
Asymptotic stability in receding horizon control is obtained under a strict pre-dissipativity assumption, in the presence of suitable state constraints. In this paper we analyze ho…
Economic MPC of Markov Decision Processes: Dissipativity in Undiscounted Infinite-Horizon Optimal Control
Sébastien Gros, Mario Zanon
Economic Model Predictive Control (MPC) dissipativity theory is central to discussing the stability of policies resulting from minimizing economic stage costs. In its current form,…
Constrained Controller and Observer Design by Inverse Optimality
Mario Zanon, Alberto Bemporad
Model Predictive Control (MPC) is often tuned by trial and error. When a baseline linear controller exists that is already well tuned in the absence of constraints and MPC is intro…
Towards Safe Reinforcement Learning Using NMPC and Policy Gradients: Part II - Deterministic Case
Sebastien Gros, Mario Zanon
In this paper, we present a methodology to deploy the deterministic policy gradient method, using actor-critic techniques, when the optimal policy is approximated using a parametri…
Real-Time Constrained Trajectory Planning and Vehicle Control for Proactive Autonomous Driving With Road Users
Ivo Batkovic, Mario Zanon, Mohammad Ali +1
For motion planning and control of autonomous vehicles to be proactive and safe, pedestrians' and other road users' motions must be considered. In this paper, we present a vehicle…
Optimality Conditions for Model Predictive Control: Rethinking Predictive Model Design
Akhil S Anand, Arash Bahari Kordabad, Mario Zanon +1
Optimality is a critical aspect of Model Predictive Control (MPC), especially in economic MPC. However, achieving optimality in MPC presents significant challenges, and may even be…
Model Predictive Control Tuning by Monte Carlo Simulation and Controller Matching
Morten Ryberg Wahlgreen, John Bagterp Jørgensen, Mario Zanon
This paper presents a systematic method for the selection of the Model Predictive Control (MPC) stage cost. We match the MPC feedback law to a proportional-integral (PI) controller…
Safe Trajectory Tracking in Uncertain Environments
Ivo Batkovic, Mohammad Ali, Paolo Falcone +1
In Model Predictive Control (MPC) formulations of trajectory tracking problems, infeasible reference trajectories and a-priori unknown constraints can lead to cumbersome designs, a…
A Feasibility-Enforcing Primal-Decomposition SQP Algorithm for Optimal Vehicle Coordination
Mario Zanon, Robert Hult, Sebastien Gros +1
In this paper we consider the problem of coordinating autonomous vehicles approaching an intersection. We cast the problem in the distributed optimisation framework and propose an…
Active Learning MPC Objective Functions from Preferences
Hasna El Hasnaouy, Pablo Krupa, Mario Zanon +1
Designing the objective function in Model Predictive Control (MPC) is challenging when performance assessment criteria are available only from human judgment. We adopt a preference…
Experimental Validation of Safe MPC for Autonomous Driving in Uncertain Environments
Ivo Batkovic, Ankit Gupta, Mario Zanon +1
The full deployment of autonomous driving systems on a worldwide scale requires that the self-driving vehicle be operated in a provably safe manner, i.e., the vehicle must be able…
Reinforcement Learning for Mixed-Integer Problems Based on MPC
Sebastien Gros, Mario Zanon
Model Predictive Control has been recently proposed as policy approximation for Reinforcement Learning, offering a path towards safe and explainable Reinforcement Learning. This ap…
A Semi-Distributed Interior Point Algorithm for Optimal Coordination of Automated Vehicles at Intersections
Robert Hult, Mario Zanon, Sebastien Gros +1
In this paper, we consider the optimal coordination of automated vehicles at intersections under fixed crossing orders. We formulate the problem using direct optimal control and ex…
A Gauss-Newton-Like Hessian Approximation for Economic NMPC
Mario Zanon
Economic Model Predictive Control (EMPC) has recently become popular because of its ability to control constrained nonlinear systems while explicitly optimizing a prescribed perfor…
A Computationally Efficient Model for Pedestrian Motion Prediction
Ivo Batkovic, Mario Zanon, Nils Lubbe +1
We present a mathematical model to predict pedestrian motion over a finite horizon, intended for use in collision avoidance algorithms for autonomous driving. The model is based on…
Computation of safe disturbance sets using implicit RPI sets
Sampath Kumar Mulagaleti, Alberto Bemporad, Mario Zanon
Given a stable linear time-invariant (LTI) system subject to output constraints, we present a method to compute a set of disturbances such that the reachable set of outputs matches…
Stabilization of strictly pre-dissipative nonlinear receding horizon control by terminal costs
Lars Grüne, Mario Zanon
It is known that receding horizon control with a strictly pre-dissipative optimal control problem yields a practically asymptotically stable closed loop when suitable state constra…
Practical Reinforcement Learning of Stabilizing Economic MPC
Mario Zanon, Sébastien Gros, Alberto Bemporad
Reinforcement Learning (RL) has demonstrated a huge potential in learning optimal policies without any prior knowledge of the process to be controlled. Model Predictive Control (MP…
Robust Control Invariance and Communication Scheduling in Lossy Wireless Networked Control Systems
Masoud Bahraini, Mario Zanon, Paolo Falcone +1
In Networked Control Systems (NCS) impairments of the communication channel can be disruptive to stability and performance. In this paper, we consider the problem of scheduling the…
Equivalence of Optimality Criteria for Markov Decision Process and Model Predictive Control
Arash Bahari Kordabad, Mario Zanon, Sebastien Gros
This paper shows that the optimal policy and value functions of a Markov Decision Process (MDP), either discounted or not, can be captured by a finite-horizon undiscounted Optimal…
Safe Reinforcement Learning Using Robust MPC
Mario Zanon, Sébastien Gros
Reinforcement Learning (RL) has recently impressed the world with stunning results in various applications. While the potential of RL is now well-established, many critical aspects…
On Piecewise Quadratic Terminal Costs for MPC
Sampath Kumar Mulagaleti, Boris Houska, Mario Zanon +1
This paper presents a novel approach to synthesize stabilizing termi- nal ingredients for linear model predictive control (MPC) schemes, with the aim of increasing the region of at…
Economic Linear Quadratic MPC With Non-Unique Optimal Solutions
Mario Zanon
Asymptotic stability in economic receding horizon control can be obtained under a strict dissipativity assumption, related to positive-definiteness of a so-called rotated cost, and…
Computation of Input Disturbance Sets for Constrained Output Reachability
Sampath Kumar Mulagaleti, Alberto Bemporad, Mario Zanon
Linear models with additive unknown-but-bounded input disturbances are extensively used to model uncertainty in robust control systems design. Typically, the disturbance set is eit…
Fast Gauss-Newton for Multiclass Cross-Entropy
Mikalai Korbit, Mario Zanon
In multiclass softmax cross-entropy, the full generalized Gauss-Newton (GGN) curvature couples all output logits through the softmax covariance, making curvature-vector products ha…
Learning for MPC with Stability & Safety Guarantees
Sébastien Gros, Mario Zanon
The combination of learning methods with Model Predictive Control (MPC) has attracted a significant amount of attention in the recent literature. The hope of this combination is to…
Model Predictive Control with Infeasible Reference Trajectories
Ivo Batkovic, Mohammad Ali, Paolo Falcone +1
Model Predictive Control (MPC) formulations are typically built on the requirement that a feasible reference trajectory is available. In practical settings, however, references tha…
Primal or Dual Terminal Constraints in Economic MPC? -- Comparison and Insights
Timm Faulwasser, Mario Zanon
This chapter compares different formulations for Economic nonlinear Model Predictive Control (EMPC) which are all based on an established dissipativity assumption on the underlying…
Towards Safe Reinforcement Learning Using NMPC and Policy Gradients: Part I - Stochastic case
Sebastien Gros, Mario Zanon
We present a methodology to deploy the stochastic policy gradient method, using actor-critic techniques, when the optimal policy is approximated using a parametric optimization pro…
Optimization-based Heuristic for Vehicle Dynamic Coordination in Mixed Traffic Intersections
Muhammad Faris, Mario Zanon, Paolo Falcone
In this paper, we address a coordination problem for connected and autonomous vehicles (CAVs) in mixed traffic settings with human-driven vehicles (HDVs). The main objective is to…
Performance Quantification of a Nonlinear Model Predictive Controller by Parallel Monte Carlo Simulations of a Closed-loop System
Morten Wahlgreen Kaysfeld, Mario Zanon, John Bagterp Jørgensen
This paper presents a parallel Monte Carlo simulation based performance quantification method for nonlinear model predictive control (NMPC) in closed-loop. The method provides dist…
Reinforcement Learning Based on Real-Time Iteration NMPC
Mario Zanon, Vyacheslav Kungurtsev, Sébastien Gros
Reinforcement Learning (RL) has proven a stunning ability to learn optimal policies from data without any prior knowledge on the process. The main drawback of RL is that it is typi…
Characterization and Computation of Feedback Nash Equilibria in Scalar Discounted N-Player Linear Quadratic Games
Chiara Cavalagli, Alberto Bemporad, Mario Zanon
This paper studies feedback Nash equilibria (FNE) in scalar discounted linear quadratic (LQ) games with players. By explicitly incorporating the discount factor, we show that f…
Learning disturbance models for offset-free reference tracking
Pablo Krupa, Mario Zanon, Alberto Bemporad
This work presents a nonlinear control framework that guarantees asymptotic offset-free tracking of generic reference trajectories by learning a nonlinear disturbance model, which…
Learning the MPC objective function from human preferences
Pablo Krupa, Hasna El Hasnaouy, Mario Zanon +1
In Model Predictive Control (MPC), the objective function plays a central role in determining the closed-loop behavior of the system, and must therefore be designed to achieve the…
A New Dissipativity Condition for Asymptotic Stability of Discounted Economic MPC
Mario Zanon, Sébastien Gros
Economic Model Predictive Control has recently gained popularity due to its ability to directly optimize a given performance criterion, while enforcing constraint satisfaction for…
A Parallel Decomposition Scheme for Solving Long-Horizon Optimal Control Problems
Sungho Shin, Timm Faulwasser, Mario Zanon +1
We present a temporal decomposition scheme for solving long-horizon optimal control problems. In the proposed scheme, the time domain is decomposed into a set of subdomains with pa…
Second-Order, First-Class: A Composable Stack for Curvature-Aware Training
Mikalai Korbit, Mario Zanon
Second-order methods promise improved stability and faster convergence, yet they remain underused due to implementation overhead, tuning brittleness, and the lack of composable API…
Data-driven Economic NMPC using Reinforcement Learning
Sébastien Gros, Mario Zanon
Reinforcement Learning (RL) is a powerful tool to perform data-driven optimal control without relying on a model of the system. However, RL struggles to provide hard guarantees on…
Exact Gauss-Newton Optimization for Training Deep Neural Networks
Mikalai Korbit, Adeyemi D. Adeoye, Alberto Bemporad +1
We present Exact Gauss-Newton (EGN), a stochastic second-order optimization algorithm that combines the generalized Gauss-Newton (GN) Hessian approximation with low-rank linear alg…
Stability-Constrained Markov Decision Processes Using MPC
Mario Zanon, Sébastien Gros, Michele Palladino
In this paper, we consider solving discounted Markov Decision Processes (MDPs) under the constraint that the resulting policy is stabilizing. In practice MDPs are solved based on s…
Model Predictive Control with Environment Adaptation for Legged Locomotion
Niraj Rathod, Angelo Bratta, Michele Focchi +4
Re-planning in legged locomotion is crucial to track the desired user velocity while adapting to the terrain and rejecting external disturbances. In this work, we propose and test…
Fast and scalable likelihood maximization for Exponential Random Graph Models with local constraints
Nicolò Vallarano, Matteo Bruno, Emiliano Marchese +5
Exponential Random Graph Models (ERGMs) have gained increasing popularity over the years. Rooted into statistical physics, the ERGMs framework has been successfully employed for re…