arXiv subjects

Shengling Shi

Publications and source records attributed to Shengling Shi.

At least 19 recordsLinked to original sources

arXiv2026

Asynchronous Model Predictive Control Under Model Mismatch: Stability and Performance Guarantees

Certainty-equivalence model predictive control (CE-MPC) is widely used for its simplicity and efficiency, but theoretical guarantees under asynchronous feedback remain limited. This paper establishes stability and performance guarantees for asynchronous CE-MPC of input-constrained nonlinear systems. We first derive a nominal stability condition and competitive-ratio bound that explicitly account for inter-execution intervals without prescribing a feedback mechanism. A value-function perturbation analysis for quadratic stage costs then accommodates additive, potentially non-smooth model mismatch without constraint qualification conditions. Combining these results yields stability criteria and competitive-ratio bounds for CE-MPC under general asynchronous feedback, including event/self-triggered and multi-step MPC. The guarantees explicitly relate prediction horizon, inter-execution time, and uncertainty magnitude, quantifying performance degradation relative to an ideal infinite-horizon controller. These results clarify tradeoffs between feedback frequency, model accuracy, and horizon length, guiding asynchronous MPC design using approximate or learned models.

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arXiv2025

Predictive control barrier functions for piecewise affine systems with non-smooth constraints

Obtaining control barrier functions (CBFs) with large safe sets for complex nonlinear systems and constraints is a challenging task. Predictive CBFs address this issue by using an online finite-horizon optimal control problem that implicitly defines a large safe set. The optimal control problem, also known as the predictive safety filter (PSF), involves predicting the system's flow under a given backup control policy. However, for non-smooth systems and constraints, some key elements, such as CBF gradients and the sensitivity of the flow, are not well-defined, making the current methods inadequate for ensuring safety. Additionally, for control-non-affine systems, the PSF is generally nonlinear and non-convex, posing challenges for real-time computation. This paper considers piecewise affine systems, which are usually control-non-affine, under nonlinear state and polyhedral input constraints. We solve the safety issue by incorporating set-valued generalized Clarke derivatives in the PSF design. We show that enforcing CBF constraints across all elements of the generalized Clarke derivatives suffices to guarantee safety. Moreover, to lighten the computational overhead, we propose an explicit approximation of the PSF. The resulting control methods are demonstrated through numerical examples.

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arXiv2025

Approximate Model Predictive Control for Microgrid Energy Management via Imitation Learning

Efficient energy management is essential for reliable and sustainable microgrid operation amid increasing renewable integration. In this paper, an imitation learning-based framework to approximate mixed-integer Economic Model Predictive Control (EMPC) is proposed for microgrid energy management, considering fuel generators, renewable energy resources, a unified energy storage unit, and curtailable loads. Within the proposed framework, a neural network is trained to imitate expert EMPC control actions from offline trajectories, thereby enabling fast real-time decision making without solving online mixed-integer optimization problems, which often exhibit highly variable solution times across instances and do not scale well to large problem sizes; in particular, worst-case solve times can be excessively large and therefore unsuitable for real-time deployment. In contrast, the learned policy provides predictable and consistently low computation times. To enhance robustness and generalization, the learning process incorporates noise injection during training to mitigate distribution shift and explicitly accounts for forecast uncertainty in renewable generation and demand. Furthermore, a constraint-tightening approach combined with a projection layer is proposed to ensure recursive feasibility and constraint satisfaction of the learned controller. Simulation results demonstrate that the learned policy achieves economic performance comparable to EMPC, while reducing computation time by approximately one order of magnitude relative to the optimization-based EMPC.

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arXiv2025

Bang-Ride Optimal Control: Monotonicity, External Positivity, and Fast Battery Charging

This work studies a class of optimal control problems with scalar inputs and general constraints, whose solutions follow a bang-ride pattern that always activates a constraint and enables efficient numerical computation. As a motivating example, fast battery charging leads to computationally demanding optimal control problems when detailed electrochemical models are used. Recently proposed optimization-free heuristics reduce this computational cost while producing input profiles observed in practice, following a bang-ride pattern and applying the maximum feasible input. We investigate when such heuristics satisfy necessary optimality conditions. By leveraging Pontryagin's maximum principle, we unify and formalize existing insights on the bang-ride structure and on the optimal control attaining the maximum feasible input under monotonicity. We further establish a novel connection between the structured optimal control and the external positivity of the costate dynamics. These results provide a rigorous theoretical foundation for heuristic charging strategies and explain the efficiency of optimization-free algorithms.

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arXiv2025

Robust Adaptive Discrete-Time Control Barrier Certificate

This work develops a robust adaptive control strategy for discrete-time systems using Control Barrier Functions (CBFs) to ensure safety under parametric model uncertainty and disturbances. A key contribution of this work is establishing a barrier function certificate in discrete time for general online parameter estimation algorithms. This barrier function certificate guarantees positive invariance of the safe set despite disturbances and parametric uncertainty without access to the true system parameters. In addition, real-time implementation and inherent robustness guarantees are provided. The proposed robust adaptive safe control framework demonstrates that the parameter estimation module can be designed separately from the CBF-based safety filter, simplifying the development of safe adaptive controllers for discrete-time systems. The resulting safe control approach guarantees that the system remains within the safe set while the controller adapts to model uncertainties, making it a promising strategy for discrete-time safety-critical systems.

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arXiv2025

From learning to safety: A Direct Data-Driven Framework for Constrained Control

Ensuring safety in the sense of constraint satisfaction for learning-based control is a critical challenge, especially in the model-free case. While safety filters address this challenge in the model-based setting by modifying unsafe control inputs, they typically rely on predictive models derived from physics or data. This reliance limits their applicability for advanced model-free learning control methods. To address this gap, we propose a new optimization-based control framework that determines safe control inputs directly from data. The benefit of the framework is that it can be updated through arbitrary model-free learning algorithms to pursue optimal performance. As a key component, the concept of direct data-driven safety filters (3DSF) is first proposed. The framework employs a novel safety certificate, called the state-action control barrier function (SACBF). We present three different schemes to learn the SACBF. Furthermore, based on input-to-state safety analysis, we present the error-to-state safety analysis framework, which provides formal guarantees on safety and recursive feasibility even in the presence of learning inaccuracies. The proposed control framework bridges the gap between model-free learning-based control and constrained control, by decoupling performance optimization from safety enforcement. Simulations on vehicle control illustrate the superior performance regarding constraint satisfaction and task achievement compared to model-based methods and reward shaping.

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arXiv2024

Certainty-Equivalence Model Predictive Control: Stability, Performance, and Beyond

Handling model mismatch is a common challenge in model predictive control (MPC). While robust MPC is effective, its conservatism often makes it less desirable. Certainty-equivalence MPC (CE-MPC), which uses a nominal model, offers an appealing alternative due to its design simplicity and low computational costs. This paper investigates CE-MPC for uncertain nonlinear systems with multiplicative parametric uncertainty and input constraints that are inactive at the steady state. The primary contributions are two-fold. First, a novel perturbation analysis of the MPC value function is provided, without assuming the Lipschitz continuity of the stage cost, better tailoring the widely used quadratic cost and having broader applicability in value function approximation, learning-based MPC, and performance-driven MPC design. Second, the stability and performance analysis of CE-MPC are provided, quantifying the suboptimality of CE-MPC compared to the infinite-horizon optimal controller with perfect model knowledge. The results provide insights in how the prediction horizon and model mismatch jointly affect stability and the worst-case performance. Furthermore, the general results are specialized to linear quadratic control, and a competitive ratio bound is derived, serving as the first competitive-ratio bound for MPC of uncertain linear systems with input constraints and multiplicative uncertainty.

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arXiv2024

Data-informativity conditions for structured linear systems with implications for dynamic networks

When estimating a single subsystem (module) in a linear dynamic network with a prediction error method, a data-informativity condition needs to be satisfied for arriving at a consistent module estimate. This concerns a condition on input signals in the constructed, possibly MIMO (multiple input multiple output) predictor model being persistently exciting, which is typically guaranteed if the input spectrum is positive definite for a sufficient number of frequencies. Generically, the condition can be formulated as a path-based condition on the graph of the network model. The current condition has two elements of possible conservatism: (a) rather than focussing on the full MIMO model, one would like to be able to focus on consistently estimating the target module only, and (b) structural information, such as structural zero elements in the interconnection structure or known subsystems, should be taken into account. In this paper relaxed conditions for data-informativity are derived addressing these two issues, leading to relaxed path-based conditions on the network graph. This leads to experimental conditions that are less strict, i.e. require a smaller number of external excitation signals. Additionally, the new expressions for data-informativity in identification are shown to be closely related to earlier derived conditions for (generic) single module identifiability.

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arXiv2024

Stability and Performance Analysis of Model Predictive Control of Uncertain Linear Systems

Model mismatch often poses challenges in model-based controller design. This paper investigates model predictive control (MPC) of uncertain linear systems with input constraints, focusing on stability and closed-loop infinite-horizon performance. The uncertainty arises from a parametric mismatch between the true and the estimated system under the matrix Frobenius norm. We examine a simple MPC controller that exclusively uses the estimated system model and establishes sufficient conditions under which the MPC controller can stabilize the true system. Moreover, we derive a theoretical performance bound based on relaxed dynamic programming, elucidating the impact of prediction horizon and modeling errors on the suboptimality gap between the MPC controller and the Oracle infinite-horizon optimal controller with knowledge of the true system. Simulations of a numerical example validate the theoretical results. Our theoretical analysis offers guidelines for obtaining the desired modeling accuracy and choosing a proper prediction horizon to develop certainty-equivalent MPC controllers for uncertain linear systems.

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arXiv2023

State-action control barrier functions: Imposing safety on learning-based control with low online computational costs

Learning-based control with safety guarantees usually requires real-time safety certification and modifications of possibly unsafe learning-based policies. The control barrier function (CBF) method uses a safety filter containing a constrained optimization problem to produce safe policies. However, finding a valid CBF for a general nonlinear system requires a complex function parameterization, which in general, makes the policy optimization problem difficult to solve in real time. For nonlinear systems with nonlinear state constraints, this paper proposes the novel concept of state-action CBFs, which not only characterize the safety at each state but also evaluate the control inputs taken at each state. State-action CBFs, in contrast to CBFs, enable a flexible parameterization, resulting in a safety filter that involves a convex quadratic optimization problem. This, in turn, significantly alleviates the online computational burden. To synthesize state-action CBFs, we propose a learning-based approach exploiting Hamilton-Jacobi reachability. The effect of learning errors on the effectiveness of state-action CBFs is addressed by constraint tightening and introducing a new concept called contractive CBFs. These contributions ensure formal safety guarantees for learned CBFs and control policies, enhancing the applicability of learning-based control in real-time scenarios. Simulation results on an inverted pendulum with elastic walls validate the proposed CBFs in terms of constraint satisfaction and CPU time.

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arXiv2023

Regret Analysis of Learning-Based Linear Quadratic Gaussian Control with Additive Exploration

In this paper, we analyze the regret incurred by a computationally efficient exploration strategy, known as naive exploration, for controlling unknown partially observable systems within the Linear Quadratic Gaussian (LQG) framework. We introduce a two-phase control algorithm called LQG-NAIVE, which involves an initial phase of injecting Gaussian input signals to obtain a system model, followed by a second phase of an interplay between naive exploration and control in an episodic fashion. We show that LQG-NAIVE achieves a regret growth rate of $\tilde{\mathcal{O}}(\sqrt{T})$, i.e., $\mathcal{O}(\sqrt{T})$ up to logarithmic factors after $T$ time steps, and we validate its performance through numerical simulations. Additionally, we propose LQG-IF2E, which extends the exploration signal to a `closed-loop' setting by incorporating the Fisher Information Matrix (FIM). We provide compelling numerical evidence of the competitive performance of LQG-IF2E compared to LQG-NAIVE.

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arXiv2023

A Behavioral Perspective on Models of Linear Dynamical Networks with Manifest Variables

Networks of dynamical systems play an important role in various domains and have motivated many studies on the control and analysis of linear dynamical networks. For linear network models considered in these studies, it is typically pre-determined what signal channels are inputs and what are outputs. These models do not capture the practical need to incorporate different experimental situations, where different selections of input and output channels are applied to the same network. Moreover, a unified view of different network models is lacking. This work makes an initial step towards addressing the above issues by taking a behavioral perspective, where input and output channels are not pre-determined. The focus of this work is on behavioral network models with only external variables. By exploiting the concept of hypergraphs, novel dual graphical representations, called system graphs and signal graphs, are introduced for behavioral networks. Moreover, connections between behavioral network models and structural vector autoregressive models are established. In addition to their connections in graphical representations, it is shown that the regularity of interconnections is an essential assumption when choosing a structural vector autoregressive model.

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arXiv2023

Approximate Dynamic Programming for Constrained Piecewise Affine Systems with Stability and Safety Guarantees

Infinite-horizon optimal control of constrained piecewise affine (PWA) systems has been approximately addressed by hybrid model predictive control (MPC), which, however, has computational limitations, both in offline design and online implementation. In this paper, we consider an alternative approach based on approximate dynamic programming (ADP), an important class of methods in reinforcement learning. We accommodate non-convex union-of-polyhedra state constraints and linear input constraints into ADP by designing PWA penalty functions. PWA function approximation is used, which allows for a mixed-integer encoding to implement ADP. The main advantage of the proposed ADP method is its online computational efficiency. Particularly, we propose two control policies, which lead to solving a smaller-scale mixed-integer linear program than conventional hybrid MPC, or a single convex quadratic program, depending on whether the policy is implicitly determined online or explicitly computed offline. We characterize the stability and safety properties of the closed-loop systems, as well as the sub-optimality of the proposed policies, by quantifying the approximation errors of value functions and policies. We also develop an offline mixed-integer linear programming-based method to certify the reliability of the proposed method. Simulation results on an inverted pendulum with elastic walls and on an adaptive cruise control problem validate the control performance in terms of constraint satisfaction and CPU time.

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arXiv2023

Suboptimality analysis of receding horizon quadratic control with unknown linear systems and its applications in learning-based control

This work analyzes how the trade-off between the modeling error, the terminal value function error, and the prediction horizon affects the performance of a nominal receding-horizon linear quadratic (LQ) controller. By developing a novel perturbation result of the Riccati difference equation, a novel performance upper bound is obtained and suggests that for many cases, the prediction horizon can be either one or infinity to improve the control performance, depending on the relative difference between the modeling error and the terminal value function error. The result also shows that when an infinite horizon is desired, a finite prediction horizon that is larger than the controllability index can be sufficient for achieving a near-optimal performance, revealing a close relation between the prediction horizon and controllability. The obtained suboptimality performance upper bound is applied to provide novel sample complexity and regret guarantees for nominal receding-horizon LQ controllers in a learning-based setting. We show that an adaptive prediction horizon that increases as a logarithmic function of time is beneficial for regret minimization.

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arXiv2022

Finite-sample analysis of identification of switched linear systems with arbitrary or restricted switching

For the identification of switched systems with a measured switching signal, this work aims to analyze the effect of switching strategies on the estimation error. The data for identification is assumed to be collected from globally asymptotically or marginally stable switched systems under switches that are arbitrary or subject to an average dwell time constraint. Then the switched system is estimated by the least-squares (LS) estimator. To capture the effect of the parameters of the switching strategies on the LS estimation error, finite-sample error bounds are developed in this work. The obtained error bounds show that the estimation error is logarithmic of the switching parameters when there are only stable modes; however, when there are unstable modes, the estimation error bound can increase linearly as the switching parameter changes. This suggests that in the presence of unstable modes, the switching strategy should be properly designed to avoid the significant increase of the estimation error.

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arXiv2022

Approximate Dynamic Programming for Constrained Linear Systems: A Piecewise Quadratic Approximation Approach

Approximate dynamic programming (ADP) faces challenges in dealing with constraints in control problems. Model predictive control (MPC) is, in comparison, well-known for its accommodation of constraints and stability guarantees, although its computation is sometimes prohibitive. This paper introduces an approach combining the two methodologies to overcome their individual limitations. The predictive control law for constrained linear quadratic regulation (CLQR) problems has been proven to be piecewise affine (PWA) while the value function is piecewise quadratic. We exploit these formal results from MPC to design an ADP method for CLQR problems. A novel convex and piecewise quadratic neural network with a local-global architecture is proposed to provide an accurate approximation of the value function, which is used as the cost-to-go function in the online dynamic programming problem. An efficient decomposition algorithm is developed to speed up the online computation. Rigorous stability analysis of the closed-loop system is conducted for the proposed control scheme under the condition that a good approximation of the value function is achieved. Comparative simulations are carried out to demonstrate the potential of the proposed method in terms of online computation and optimality.

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arXiv2022

Identifiability in Dynamic Acyclic Networks with Partial Excitations and Measurements

This paper deals with dynamic networks in which the causality relations between the vertex signals are represented by linear time-invariant transfer functions (modules). Considering an acyclic network where only a subset of its vertices are measured and a subset of the vertices are excited, we explore conditions under which all the modules are identifiable on the basis of measurement data. Two sufficient conditions are presented in the paper, where the first condition concerns an identifiability analysis that needs to be performed for each vertex, while the second condition, based on the concept of tree/anti-tree covering, results from a graphical synthesis approach to allocate actuators and sensors in an acyclic network for achieving generic identifiability.

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arXiv2021

Single module identifiability in linear dynamic networks with partial excitation and measurement

Identifiability of a single module in a network of transfer functions is determined by whether a particular transfer function in the network can be uniquely distinguished within a network model set, on the basis of data. Whereas previous research has focused on the situations that all network signals are either excited or measured, we develop generalized analysis results for the situation of partial measurement and partial excitation. As identifiability conditions typically require a sufficient number of external excitation signals, this work introduces a novel network model structure such that excitation from unmeasured noise signals is included, which leads to less conservative identifiability conditions than relying on measured excitation signals only. More importantly, graphical conditions are developed to verify global and generic identifiability of a single module based on the topology of the dynamic network. Depending on whether the input or the output of the module can be measured, we present four identifiability conditions which cover all possible situations in single module identification. These conditions further lead to synthesis approaches for allocating excitation signals and selecting measured signals, to warrant single module identifiability. In addition, if the identifiability conditions are satisfied, indirect identification methods are developed to provide a consistent estimate of the module. All the obtained results are also extended to identifiability of multiple modules in the network.

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