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1. Finite Sample Identification of Partially Observed Bilinear Dynamical Systems

   Sattar, Yahya; Jedra, Yassir; Fazel, Maryam; Dean, Sarah (May 2025, Proceedings of Machine Learning Research)

   Ozay, N; Balzano, L; Panagou, D; Abate, A (Ed.)

   We consider the problem of learning a realization of a partially observed bilinear dynamical system (BLDS) from noisy input-output data. Given a single trajectory of input-output samples, we provide an algorithm and a finite time analysis for learning the system’s Markov-like parameters, from which a balanced realization of the bilinear system can be obtained. The stability of BLDS depends on the sequence of inputs used to excite the system. Moreover, our identification algorithm regresses the outputs to highly correlated, nonlinear, and heavy-tailed covariates. These properties, unique to partially observed bilinear dynamical systems, pose significant challenges to the analysis of our algorithm for learning the unknown dynamics. We address these challenges and provide high probability error bounds on our identification algorithm under a uniform stability assumption. Our analysis provides insights into system theoretic quantities that affect learning accuracy and sample complexity. Lastly, we perform numerical experiments with synthetic data to reinforce these insights. 

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2. Fast and Guaranteed Safe Controller Synthesis for Nonlinear Vehicle Models

   https://doi.org/10.1007/978-3-030-53288-8\_31  

   Fan, Chuchu; Miller, Kristina; Mitra, Sayan (July 2020, Computer Aided Verification - 32nd International Conference, {CAV} 2020, Los Angeles, CA, USA, July 21-24, 2020, Proceedings, Part {I})

   We address the problem of synthesizing a controller for nonlinear systems with reach-avoid requirements. Our controller consists of a reference controller and a tracking controller which drives the actual trajectory to follow the reference trajectory. We identify a type of reference trajectory such that the tracking error between the actual trajectory of the closed-loop system and the reference trajectory can be bounded. Moreover, such a bound on the tracking error is independent of the reference trajectory. Using such bounds on the tracking error, we propose a method that can find a reference trajectory by solving a satisfiability problem over linear constraints. Our overall algorithm guarantees that the resulting controller can make sure every trajectory from the initial set of the system satisfies the given reach-avoid requirement. We also implement our technique in a tool FACTEST. We show that FACTEST can find controllers for four vehicle models (3–6 dimensional state space and 2–4 dimensional input space) across eight scenarios (with up to 22 obstacles), all with running time at the sub-second range. 

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3. Model reference adaptive control for nonlinear time‐varying hybrid dynamical systems

   https://doi.org/10.1002/acs.3631  

   L'Afflitto, Andrea (August 2023, International Journal of Adaptive Control and Signal Processing)

   M. Grimble (Ed.)

   Summary This paper presents the first model reference adaptive control system for nonlinear, time‐varying, hybrid dynamical plants affected by matched and parametric uncertainties, whose resetting events are unknown functions of time and the plant's state. In addition to a control law and an adaptive law, which resemble those of the classical model reference adaptive control framework for continuous‐time dynamical systems, the proposed framework allows imposing instantaneous variations in the reference model's trajectory to rapidly steer the trajectory tracking error to zero, while retaining the closed‐loop system's ability to follow a user‐defined signal. These results are enabled by the first extension of the classical LaSalle–Yoshizawa theorem to time‐varying hybrid dynamical systems, which is presented in this paper as well. A numerical simulation shows the key features of the proposed adaptive control system and highlights its ability to reduce both the control effort and the trajectory tracking error over a classical model reference adaptive control system applied to the same problem. 

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4. Autonomous UAV with Learned Trajectory Generation and Control

   https://doi.org/10.1109/SiPS47522.2019.9020508  

   Li, Yilan; Li, Mingyang; Sanyal, Amit; Wang, Yanzhi; Qiu, Qinru (October 2019, IEEE Workshop on Signal Processing Systems (SIPS))

   Unmanned aerial vehicle (UAV) technology is a rapidly growing field with tremendous opportunities for research and applications. To achieve true autonomy for UAVs in the absence of remote control, external navigation aids like global navigation satellite systems and radar systems, a minimum energy trajectory planning that considers obstacle avoidance and stability control will be the key. Although this can be formulated as a constrained optimization problem, due to the complicated non-linear relationships between UAV trajectory and thrust control, it is almost impossible to be solved analytically. While deep reinforcement learning is known for its ability to provide model free optimization for complex system through learning, its state space, actions and reward functions must be designed carefully. This paper presents our vision of different layers of autonomy in a UAV system, and our effort in generating and tracking the trajectory both using deep reinforcement learning (DRL). The experimental results show that compared to conventional approaches, the learned trajectory will need 20% less control thrust and 18% less time to reach the target. Furthermore, using the control policy learning by DRL, the UAV will achieve 58.14% less position error and 21.77% less system power. 

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5. Implicit Trajectory Planning for Feedback Linearizable Systems: A Time-varying Optimization Approach

   https://doi.org/10.23919/ACC45564.2020.9147997  

   Zheng, Tianqi; Simpson-Porco, John; Mallada, Enrique (July 2020, American Control Conference)

   We develop an optimization-based framework for joint real-time trajectory planning and feedback control of feedback-linearizable systems. To achieve this goal, we define a target trajectory as the optimal solution of a time-varying optimization problem. In general, however, such trajectory may not be feasible due to , e.g., nonholonomic constraints. To solve this problem, we design a control law that generates feasible trajectories that asymptotically converge to the target trajectory. More precisely, for systems that are (dynamic) full-state linearizable, the proposed control law implicitly transforms the nonlinear system into an optimization algorithm of sufficiently high order. We prove global exponential convergence to the target trajectory for both the optimization algorithm and the original system. We illustrate the effectiveness of our proposed method on multi-target or multi-agent tracking problems with constraints. 

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