arXiv subjects

Tyler H. Summers

Publications and source records attributed to Tyler H. Summers.

At least 19 recordsLinked to original sources

arXiv2026

Best Response Dynamics for Zero-Sum Dynamic Games with Partial-Asymmetric Information

This work studies a class of zero-sum stochastic linear quadratic dynamic games (LQDGs) under partial and asymmetric information. Information asymmetry introduces fundamental challenges related to \textit{belief representation} and \textit{theory of mind}, where players must impute belief states and estimates of other players to inform their strategies. Existing work highlights the difficulty of applying dynamic programming-like decomposition approach to these problems. An alternative approach based on \textit{best response dynamics} is proposed, which provides insights into belief representation and theory of mind challenges. Explicit expressions for each player's best response within the class of pure linear dynamic output feedback control strategies are derived, where the internal state dimension of each control is an integer multiple of the system state dimension. As players iteratively update their best responses, they form increasingly higher-order belief states, leading to infinite-dimensional internal states. However, numerical results reveal that the game's value converges after only a few iterations, suggesting that higher-order belief states provide vanishing benefit. This work further conducts numerical experiments to analyze the impact of asymmetric beliefs, belief orders, relative controllability and observability, and direct feed-through on a linear quadratic pursuit-evasion game's value.

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arXiv2026

A Framework for Motion Planning with Temporal Logic Precedence Specifications via Augmented Graphs of Convex Sets

We present a framework for planning trajectories that avoid obstacles and satisfy logical precedence constraints expressed with a fragment of signal temporal logic (STL). Our approach models environments containing obstacles, keys, and doors, where collecting a key unlocks its associated door and potentially opens shorter paths to a goal. Based on an exact convex partitioning of the free space that encodes connectivity among convex free space, key, and door regions, we construct an augmented graph of convex sets (GCS) whose layered structure exactly encodes the key-door precedence logic. A shortest path in the augmented GCS simultaneously selects an optimal key collection sequence and computes an optimal continuous trajectory, providing an exact solution up to a finite B\'ezier curve parameterization.

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arXiv2025

Best Response Convergence for Zero-sum Stochastic Dynamic Games with Partial and Asymmetric Information

We analyze best response dynamics for finding a Nash equilibrium of an infinite horizon zero-sum stochastic linear quadratic dynamic game (LQDG) with partial and asymmetric information. We derive explicit expressions for each player's best response within the class of pure linear dynamic output feedback control strategies where the internal state dimension of each control strategy is an integer multiple of the system state dimension. With each best response, the players form increasingly higher-order belief states, leading to infinite-dimensional internal states. However, we observe in extensive numerical experiments that the game's value converges after just a few iterations, suggesting that strategies associated with increasingly higher-order belief states eventually provide no benefit. To help explain this convergence, our numerical analysis reveals rapid decay of the controllability and observability Gramian eigenvalues and Hankel singular values in higher-order belief dynamics, indicating that the higher-order belief dynamics become increasingly difficult for both players to control and observe. Consequently, the higher-order belief dynamics can be closely approximated by low-order belief dynamics with bounded error, and thus feedback strategies with limited internal state dimension can closely approximate a Nash equilibrium.

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arXiv2024

A Policy Iteration Algorithm for N-player General-Sum Linear Quadratic Dynamic Games

We present a policy iteration algorithm for the infinite-horizon N-player general-sum deterministic linear quadratic dynamic games and compare it to policy gradient methods. We demonstrate that the proposed policy iteration algorithm is distinct from the Gauss-Newton policy gradient method in the N-player game setting, in contrast to the single-player setting where under suitable choice of step size they are equivalent. We illustrate in numerical experiments that the convergence rate of the proposed policy iteration algorithm significantly surpasses that of the Gauss-Newton policy gradient method and other policy gradient variations. Furthermore, our numerical results indicate that, compared to policy gradient methods, the convergence performance of the proposed policy iteration algorithm is less sensitive to the initial policy and changes in the number of players.

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arXiv2023

Distributionally Robust CVaR-Based Safety Filtering for Motion Planning in Uncertain Environments

Safety is a core challenge of autonomous robot motion planning, especially in the presence of dynamic and uncertain obstacles. Many recent results use learning and deep learning-based motion planners and prediction modules to predict multiple possible obstacle trajectories and generate obstacle-aware ego robot plans. However, planners that ignore the inherent uncertainties in such predictions incur collision risks and lack formal safety guarantees. In this paper, we present a computationally efficient safety filtering solution to reduce the collision risk of ego robot motion plans using multiple samples of obstacle trajectory predictions. The proposed approach reformulates the collision avoidance problem by computing safe halfspaces based on obstacle sample trajectories using distributionally robust optimization (DRO) techniques. The safe halfspaces are used in a model predictive control (MPC)-like safety filter to apply corrections to the reference ego trajectory thereby promoting safer planning. The efficacy and computational efficiency of our approach are demonstrated through numerical simulations.

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arXiv2022

An Online Joint Optimization-Estimation Architecture for Distribution Networks

In this paper, we propose an optimal control-estimation architecture for distribution networks, which jointly solves the optimal power flow (OPF) problem and static state estimation (SE) problem through an online gradient-based feedback algorithm. The main objective is to enable a fast and timely interaction between the optimal controllers and state estimators with limited sensor measurements. First, convergence and optimality of the proposed algorithm are analytically established. Then, the proposed gradient-based algorithm is modified by introducing statistical information of the inherent estimation and linearization errors for an improved and robust performance of the online control decisions. Overall, the proposed method eliminates the traditional separation of control and operation, where control and estimation usually operate at distinct layers and different time-scales. Hence, it enables a computationally affordable, efficient and robust online operational framework for distribution networks under time-varying settings.

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arXiv2022

Optimal Power Flow with State Estimation In the Loop for Distribution Networks

We propose a framework for integrating optimal power flow (OPF) with state estimation (SE) in the loop for distribution networks. Our approach combines a primal-dual gradient-based OPF solver with a SE feedback loop based on a limited set of sensors for system monitoring, instead of assuming exact knowledge of all states. The estimation algorithm reduces uncertainty on unmeasured grid states based on a few appropriate online state measurements and noisy "pseudo-measurements". We analyze the convergence of the proposed algorithm and quantify the statistical estimation errors based on a weighted least squares (WLS) estimator. The numerical results on a 4521-node network demonstrate that this approach can scale to extremely large networks and provide robustness to both large pseudo measurement variability and inherent sensor measurement noise.

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arXiv2022

Risk-Bounded Temporal Logic Control of Continuous-Time Stochastic Systems

Motivated by the recent interest in risk-aware control, we study a continuous-time control synthesis problem to bound the risk that a stochastic linear system violates a given specification. We use risk signal temporal logic as a specification formalism in which distributionally robust risk predicates are considered and equipped with the usual Boolean and temporal operators. Our control approach relies on reformulating these risk predicates as deterministic predicates over mean and covariance states of the system. We then obtain a timed sequence of sets of mean and covariance states from the timed automata representation of the specification. To avoid an explosion in the number of automata states, we propose heuristics to find candidate sequences effectively. To execute and check dynamic feasibility of these sequences, we present a sampled-data control technique based on time discretization and constraint tightening that allows to perform timed transitions while satisfying the continuous-time constraints.

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arXiv2022

Policy Iteration for Multiplicative Noise Output Feedback Control

We propose a policy iteration algorithm for solving the multiplicative noise linear quadratic output feedback design problem. The algorithm solves a set of coupled Riccati equations for estimation and control arising from a partially observable Markov decision process (POMDP) under a class of linear dynamic control policies. We show in numerical experiments far faster convergence than a value iteration algorithm, formerly the only known algorithm for solving this class of problem. The results suggest promising future research directions for policy optimization algorithms in more general POMDPs, including the potential to develop novel approximate data-driven approaches when model parameters are not available.

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arXiv2021

Anomaly Detection Under Multiplicative Noise Model Uncertainty

State estimators are crucial components of anomaly detectors that are used to monitor cyber-physical systems. Many frequently-used state estimators are susceptible to model risk as they rely critically on the availability of an accurate state-space model. Modeling errors make it more difficult to distinguish whether deviations from expected behavior are due to anomalies or simply a lack of knowledge about the system dynamics. In this research, we account for model uncertainty through a multiplicative noise framework. Specifically, we propose to use the multiplicative noise LQG based compensator in this setting to hedge against the model uncertainty risk. The size of the residual from the estimator can then be compared against a threshold to detect anomalies. Finally, the proposed detector is validated using numerical simulations. Extension of state-of-the-art anomaly detection in cyber-physical systems to handle model uncertainty represents the main novel contribution of the present work.

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arXiv2021

Risk-Averse RRT* Planning with Nonlinear Steering and Tracking Controllers for Nonlinear Robotic Systems Under Uncertainty

We propose a two-phase risk-averse architecture for controlling stochastic nonlinear robotic systems. We present Risk-Averse Nonlinear Steering RRT* (RANS-RRT*) as an RRT* variant that incorporates nonlinear dynamics by solving a nonlinear program (NLP) and accounts for risk by approximating the state distribution and performing a distributionally robust (DR) collision check to promote safe planning. The generated plan is used as a reference for a low-level tracking controller. We demonstrate three controllers: finite horizon linear quadratic regulator (LQR) with linearized dynamics around the reference trajectory, LQR with robustness-promoting multiplicative noise terms, and a nonlinear model predictive control law (NMPC). We demonstrate the effectiveness of our algorithm using unicycle dynamics under heavy-tailed Laplace process noise in a cluttered environment.

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arXiv2021

Higher-Order Moment-Based Anomaly Detection

The identification of anomalies is a critical component of operating complex, and possibly large-scale and geo-graphically distributed cyber-physical systems. While designing anomaly detectors, it is common to assume Gaussian noise models to maintain tractability; however, this assumption can lead to the actual false alarm rate being significantly higher than expected. Here we design a distributionally robust threshold of detection using finite and fixed higher-order moments of the detection measure data such that it guarantees the actual false alarm rate to be upper bounded by the desired one. Further, we bound the states reachable through the action of a stealthy attack and identify the trade-off between this impact of attacks that cannot be detected and the worst-case false alarm rate. Through numerical experiments, we illustrate how knowledge of higher-order moments results in a tightened threshold, thereby restricting an attacker's potential impact.

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arXiv2020

Revisiting the Water Quality Sensor Placement Problem: Optimizing Network Observability and State Estimation Metrics

Real-time water quality (WQ) sensors in water distribution networks (WDN) have the potential to enable network-wide observability of water quality indicators, contamination event detection, and closed-loop feedback control of WQ dynamics. To that end, prior research has investigated a wide range of methods that guide the geographic placement of WQ sensors. These methods assign a metric for fixed sensor placement (SP) followed by \textit{metric-optimization} to obtain optimal SP. These metrics include minimizing intrusion detection time, minimizing the expected population and amount of contaminated water affected by an intrusion event. In contrast to the literature, the objective of this paper is to provide a computational method that considers the overlooked metric of state estimation and network-wide observability of the WQ dynamics. This metric finds the optimal WQ sensor placement that minimizes the state estimation error via the Kalman filter for noisy WQ dynamics -- a metric that quantifies WDN observability. To that end, the state-space dynamics of WQ states for an entire WDN are given and the observability-driven sensor placement algorithm is presented. The algorithm takes into account the time-varying nature of WQ dynamics due to changes in the hydraulic profile -- a collection of hydraulic states including heads (pressures) at nodes and flow rates in links which are caused by a demand profile over a certain period of time. Thorough case studies are given, highlighting key findings, observations, and recommendations for WDN operators. Github codes are included for reproducibility.

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arXiv2020

Robust Distributed Planar Formation Control for Higher-Order Holonomic and Nonholonomic Agents

We present a distributed formation control strategy for agents with a variety of dynamics to achieve a desired planar formation. Our approach is based on the barycentric-coordinate-based (BCB) control, which is fully distributed, does not require inter-agent communication or a common sense of orientation, and can be implemented using relative position measurements acquired by agents in their local coordinate frames. This removes the need for global positioning or alignment of local coordinate frames, which are required across several existing strategies. We show how the BCB control for agents with the simplest dynamical model, i.e., the single-integrator dynamics, can be extended to agents with higher-order dynamics such as quadrotors, and nonholonomic agents such as unicycles and cars. Specifically, our extension preserves the desired convergence and robustness guarantees of the BCB approach and is provably robust to saturations in the input and unmodeled linear actuator dynamics for unicycle and car agents. We further show that under our proposed BCB control design, the agents can move along a rotated and scaled control direction without affecting the convergence to the desired formation. This observation is used to design a fully distributed collision avoidance strategy, which is often not considered in the formation control literature. We demonstrate the proposed approach in simulations and further present a distributed robotic platform to test the strategy experimentally. Our experimental platform consists of off-the-shelf equipment that can be used to test and validate other multi-agent algorithms. The code and implementation instructions for this platform are available online.

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arXiv2020

Trust-based user-interface design for human-automation systems

We present a method for dynamics-driven, user-interface design for a human-automation system via sensor selection. We define the user-interface to be the output of a MIMO LTI system, and formulate the design problem as one of selecting an output matrix from a given set of candidate output matrices. Sufficient conditions for situation awareness are captured as additional constraints on the selection of the output matrix. These constraints depend upon the level of trust the human has in the automation. We show that the resulting user-interface design problem is a combinatorial, set-cardinality minimization problem with set function constraints. We propose tractable algorithms to compute optimal or sub-optimal solutions with suboptimality bounds. Our approaches exploit monotonicity and submodularity present in the design problem, and rely on constraint programming and submodular maximization. We apply this method to the IEEE 118-bus, to construct correct-by-design interfaces under various operating scenarios.

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arXiv2020

Towards Integrated Perception and Motion Planning with Distributionally Robust Risk Constraints

Safely deploying robots in uncertain and dynamic environments requires a systematic accounting of various risks, both within and across layers in an autonomy stack from perception to motion planning and control. Many widely used motion planning algorithms do not adequately incorporate inherent perception and prediction uncertainties, often ignoring them altogether or making questionable assumptions of Gaussianity. We propose a distributionally robust incremental sampling-based motion planning framework that explicitly and coherently incorporates perception and prediction uncertainties. We design output feedback policies and consider moment-based ambiguity sets of distributions to enforce probabilistic collision avoidance constraints under the worst-case distribution in the ambiguity set. Our solution approach, called Output Feedback Distributionally Robust $RRT^{*}$(OFDR-$RRT^{*})$, produces asymptotically optimal risk-bounded trajectories for robots operating in dynamic, cluttered, and uncertain environments, explicitly incorporating mapping and localization error, stochastic process disturbances, unpredictable obstacle motion, and uncertain obstacle locations. Numerical experiments illustrate the effectiveness of the proposed algorithm.

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arXiv2019

Distributionally Robust Tuning of Anomaly Detectors in Cyber-Physical Systems with Stealthy Attacks

Designing resilient control strategies for mitigating stealthy attacks is a crucial task in emerging cyber-physical systems. In the design of anomaly detectors, it is common to assume Gaussian noise models to maintain tractability; however, this assumption can lead the actual false alarm rate to be significantly higher than expected. We propose a distributionally robust anomaly detector for noise distributions in moment-based ambiguity sets. We design a detection threshold that guarantees that the actual false alarm rate is upper bounded by the desired one by using generalized Chebyshev inequalities. Furthermore, we highlight an important trade-off between the worst-case false alarm rate and the potential impact of a stealthy attacker by efficiently computing an outer ellipsoidal bound for the attack-reachable states corresponding to the distributionally robust detector threshold. We illustrate this trade-off with a numerical example and compare the proposed approach with a traditional chi-squared detector.

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arXiv2019

A Performance and Stability Analysis of Low-inertia Power Grids with Stochastic System Inertia

Traditional synchronous generators with rotational inertia are being replaced by low-inertia renewable energy resources (RESs) in many power grids and operational scenarios. Due to emerging market mechanisms, inherent variability of RESs, and existing control schemes, the resulting system inertia levels can not only be low but also markedly time-varying. In this paper, we investigate performance and stability of low-inertia power systems with stochastic system inertia. In particular, we consider system dynamics modelled by a linearized stochastic swing equation, where stochastic system inertia is regarded as multiplicative noise. The $\mathcal{H}_2$ norm is used to quantify the performance of the system in the presence of persistent disturbances or transient faults. The performance metric can be computed by solving a generalized Lyapunov equation, which has fundamentally different characteristics from systems with only additive noise. For grids with uniform inertia and damping parameters, we derive closed-form expressions for the $\mathcal{H}_2$ norm of the proposed stochastic swing equation. The analysis gives insights into how the $\mathcal{H}_2$ norm of the stochastic swing equation depends on 1) network topology; 2) system parameters; and 3) distribution parameters of disturbances. A mean-square stability condition is also derived. Numerical results provide additional insights for performance and stability of the stochastic swing equation.

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