BZPEERReading, trust and collaboration for research
Menu

Discover

GraphFollow connections around a paper, topic or saved view.

Workspaces

HomePick up where your research flow left off.InboxHandle requests, replies and notifications from one place.CollectionsCurate reading lists, evidence sets and shareable dossiers.ResearchSee your private provenance graph, trail and imports.CollaborationMove from discovery into focused discussion rooms.PublishDraft, preview and publish full-text research articles.

Network

ExpertsFind specialists worth following or asking for help.CommunitiesJoin research circles organized around shared work.PartnersSee external organizations active around the same topics.

Opportunities

ListingsBrowse roles, calls and collaborations with clearer fit signals.

Account

Log inReturn to your reading and collaboration workspace.Create accountStart saving work, following people and joining teams.
Log inCreate account

Researcher profile

Mario Zanon

Mario Zanon contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Systems and Controleess.SYmath.OCMachine LearningArtificial Intelligence

Trust snapshot

Quick read

Trust 21 - EmergingVerification L1Unclaimed author
13works
0followers
5topics
4close collaborators

Actions

Decide how to stay connected

Follow researcher0

Identity and collaboration

How to connect with this researcher

Claiming links this public author record to a researcher profile and unlocks direct collaboration workflows.

Log in to claim

Direct collaboration

Open a focused conversation when the fit is right

Claim this author entity first to unlock direct invitations.

Research graph

See the researcher in context

Open full explorer

Inspect adjacent work, topics, institutions and collaborators without jumping out to a separate graph page.

Building this graph slice

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Published work

13 published item(s)

preprint2026arXiv

Fast Gauss-Newton for Multiclass Cross-Entropy

In multiclass softmax cross-entropy, the full generalized Gauss-Newton (GGN) curvature couples all output logits through the softmax covariance, making curvature-vector products harder to scale as the number of classes grows. We show that the standard multiclass GGN can be decomposed exactly into a true-vs-rest term and a positive semidefinite within-competitor covariance term. Fast Gauss-Newton (FGN) retains the first term and drops the second, yielding a positive semidefinite under-approximation of the multiclass GGN that is exact for binary classification. The derivation uses an exact true-vs-rest scalar-margin representation of softmax cross-entropy: the loss and gradient are unchanged, and the approximation enters only at the curvature level. Exploiting the FGN curvature structure, the damped update can be written as an equivalent whitened row-space system with one row per mini-batch example. We solve this system matrix-free by conjugate gradient using Jacobian-vector and vector-Jacobian products of the scalar margin map. Targeted mechanism experiments and an evaluation on a fixed-feature multiclass head support the predictions from the decomposition: FGN stays closest to the full softmax GGN when competitor mass is concentrated or damping is large, and deviates as the dropped within-competitor covariance grows.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A New Dissipativity Condition for Asymptotic Stability of Discounted Economic MPC

Economic Model Predictive Control has recently gained popularity due to its ability to directly optimize a given performance criterion, while enforcing constraint satisfaction for nonlinear systems. Recent research has developed both numerical algorithms and stability analysis for the undiscounted case. The introduction of a discount factor in the cost, however, can be desirable in some cases of interest, e.g., economics, stochastically terminating processes, Markov decision processes, etc. Unfortunately, the stability theory in this case is still not fully developed. In this paper we propose a new dissipativity condition to prove asymptotic stability in the infinite horizon case and we connect our results with existing ones in the literature on discounted economic optimal control. Numerical examples are provided to illustrate the theoretical results.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Economic MPC of Markov Decision Processes: Dissipativity in Undiscounted Infinite-Horizon Optimal Control

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, the dissipativity theory for economic MPC applies to problems based on deterministic dynamics or to very specific classes of stochastic problems, and does not readily extend to generic Markov Decision Processes. In this paper, we clarify the core reason for this difficulty, and propose a generalization of the economic MPC dissipativity theory that circumvents it. This generalization focuses on undiscounted infinite-horizon problems and is based on nonlinear stage cost functionals, allowing one to discuss the Lyapunov asymptotic stability of policies for Markov Decision Processes in terms of the probability measures underlying their stochastic dynamics. This theory is illustrated for the stochastic Linear Quadratic Regulator with Gaussian process noise, for which a storage functional can be provided explicitly. For the sake of brevity, we limit our discussion to undiscounted Markov Decision Processes.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Learning for MPC with Stability & Safety Guarantees

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 reduce the reliance of MPC schemes on accurate models, and to tap into the fast developing machine learning and reinforcement learning tools to exploit the growing amount of data available for many systems. In particular, the combination of reinforcement learning and MPC has been proposed as a viable and theoretically justified approach to introduce explainable, safe and stable policies in reinforcement learning. However, a formal theory detailing how the safety and stability of an MPC-based policy can be maintained through the parameter updates delivered by the learning tools is still lacking. This paper addresses this gap. The theory is developed for the generic Robust MPC case, and applied in simulation in the robust tube-based linear MPC case, where the theory is fairly easy to deploy in practice. The paper focuses on Reinforcement Learning as a learning tool, but it applies to any learning method that updates the MPC parameters online.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Computation of Input Disturbance Sets for Constrained Output Reachability

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 either assumed to be known a priori or estimated from data through set-membership identification. However, the problem of computing a suitable input disturbance set in case the set of possible output values is assigned a priori has received relatively little attention. This problem arises in many contexts, such as in supervisory control, actuator design, decentralized control, and others. In this paper, we propose a method to compute input disturbance sets (and the corresponding set of states) such that the resulting set of outputs matches as closely as possible a given set of outputs, while additionally satisfying strict (inner or outer) inclusion constraints. We formulate the problem as an optimization problem by relying on the concept of robust invariance. The effectiveness of the approach is demonstrated in numerical examples that illustrate how to solve safe reference set and input-constraint set computation problems.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Stability-Constrained Markov Decision Processes Using MPC

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 some form of policy approximation. We will leverage recent results proposing to use Model Predictive Control (MPC) as a structured policy in the context of Reinforcement Learning to make it possible to introduce stability requirements directly inside the MPC-based policy. This will restrict the solution of the MDP to stabilizing policies by construction. The stability theory for MPC is most mature for the undiscounted MPC case. Hence, we will first show in this paper that stable discounted MDPs can be reformulated as undiscounted ones. This observation will entail that the MPC-based policy with stability requirements will produce the optimal policy for the discounted MDP if it is stable, and the best stabilizing policy otherwise.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Primal or Dual Terminal Constraints in Economic MPC? -- Comparison and Insights

This chapter compares different formulations for Economic nonlinear Model Predictive Control (EMPC) which are all based on an established dissipativity assumption on the underlying Optimal Control Problem (OCP). This includes schemes with and without stabilizing terminal constraints, respectively, or with stabilizing terminal costs. We recall that a recently proposed approach based on gradient correcting terminal penalties implies a terminal constraint on the adjoints of the OCP. We analyze the feasibility implications of these dual/adjoint terminal constraints and we compare our findings to approaches with and without primal terminal constraints. Moreover, we suggest a conceptual framework for approximation of the minimal stabilizing horizon length. Finally, we illustrate our findings considering a chemical reactor as an example.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Reinforcement Learning Based on Real-Time Iteration NMPC

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 typically very difficult to guarantee stability and safety. On the other hand, Nonlinear Model Predictive Control (NMPC) is an advanced model-based control technique which does guarantee safety and stability, but only yields optimality for the nominal model. Therefore, it has been recently proposed to use NMPC as a function approximator within RL. While the ability of this approach to yield good performance has been demonstrated, the main drawback hindering its applicability is related to the computational burden of NMPC, which has to be solved to full convergence. In practice, however, computationally efficient algorithms such as the Real-Time Iteration (RTI) scheme are deployed in order to return an approximate NMPC solution in very short time. In this paper we bridge this gap by extending the existing theoretical framework to also cover RL based on RTI NMPC. We demonstrate the effectiveness of this new RL approach with a nontrivial example modeling a challenging nonlinear system subject to stochastic perturbations with the objective of optimizing an economic cost.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Reinforcement Learning for Mixed-Integer Problems Based on MPC

Model Predictive Control has been recently proposed as policy approximation for Reinforcement Learning, offering a path towards safe and explainable Reinforcement Learning. This approach has been investigated for Q-learning and actor-critic methods, both in the context of nominal Economic MPC and Robust (N)MPC, showing very promising results. In that context, actor-critic methods seem to be the most reliable approach. Many applications include a mixture of continuous and integer inputs, for which the classical actor-critic methods need to be adapted. In this paper, we present a policy approximation based on mixed-integer MPC schemes, and propose a computationally inexpensive technique to generate exploration in the mixed-integer input space that ensures a satisfaction of the constraints. We then propose a simple compatible advantage function approximation for the proposed policy, that allows one to build the gradient of the mixed-integer MPC-based policy.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Robust Control Invariance and Communication Scheduling in Lossy Wireless Networked Control Systems

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 access to limited communication resources for a number of decoupled closed-loop systems subject to state and input constraint. The control objective is to preserve the invariance property of local state and input sets, such that constraint satisfaction can be guaranteed. Offline and online, state feedback scheduling policies are proposed and illustrated through numerical examples, also in case the network is subject to packet losses.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Safe Reinforcement Learning via Projection on a Safe Set: How to Achieve Optimality?

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 the safety of RL with respect to safety-critical systems is a very active research topic. Some recent contributions propose to rely on projections of the inputs delivered by the learned policy into a safe set, ensuring that the system safety is never jeopardized. Unfortunately, it is unclear whether this operation can be performed without disrupting the learning process. This paper addresses this issue. The problem is analysed in the context of $Q$-learning and policy gradient techniques. We show that the projection approach is generally disruptive in the context of $Q$-learning though a simple alternative solves the issue, while simple corrections can be used in the context of policy gradient methods in order to ensure that the policy gradients are unbiased. The proposed results extend to safe projections based on robust MPC techniques.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

A Parallel Decomposition Scheme for Solving Long-Horizon Optimal Control Problems

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 partially overlapping regions. Subproblems associated with the subdomains are solved in parallel to obtain local primal-dual trajectories that are assembled to obtain the global trajectories. We provide a sufficient condition that guarantees convergence of the proposed scheme. This condition states that the effect of perturbations on the boundary conditions (i.e., initial state and terminal dual/adjoint variable) should decay asymptotically as one moves away from the boundaries. This condition also reveals that the scheme converges if the size of the overlap is sufficiently large and that the convergence rate improves with the size of the overlap. We prove that linear quadratic problems satisfy the asymptotic decay condition, and we discuss numerical strategies to determine if the condition holds in more general cases. We draw upon a non-convex optimal control problem to illustrate the performance of the proposed scheme.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Data-driven Economic NMPC using Reinforcement Learning

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 the behavior of the resulting control scheme. In contrast, Nonlinear Model Predictive Control (NMPC) and Economic NMPC (ENMPC) are standard tools for the closed-loop optimal control of complex systems with constraints and limitations, and benefit from a rich theory to assess their closed-loop behavior. Unfortunately, the performance of (E)NMPC hinges on the quality of the model underlying the control scheme. In this paper, we show that an (E)NMPC scheme can be tuned to deliver the optimal policy of the real system even when using a wrong model. This result also holds for real systems having stochastic dynamics. This entails that ENMPC can be used as a new type of function approximator within RL. Furthermore, we investigate our results in the context of ENMPC and formally connect them to the concept of dissipativity, which is central for the ENMPC stability. Finally, we detail how these results can be used to deploy classic RL tools for tuning (E)NMPC schemes. We apply these tools on both a classical linear MPC setting and a standard nonlinear example from the ENMPC literature.

0 citations0 reviewsNo code linkedOpen access