Automated Stability Analysis of Piecewise Affine Dynamics Using Vertices

This paper presents an automated algorithm to analyze the stability of piecewise affine (PWA) dynamical systems due to their broad applications. We parametrize the Lyapunov function as a PWA function, with polytopic regions defined by the PWA dynamics. Using this parametrization, Stability conditions can be expressed as linear constraints restricted to polytopes so that the search for a Lyapunov function involves solving a linear program. However, a valid Lyapunov function might not be found given these polytopic regions. A natural response is to increase the size of the parametrization of the Lyapunov function by dividing regions and solving the new linear program. This paper proposes two new methods to divide each polytope into smaller ones. The first approach divides a polytope based on the sign of the derivative of the candidate Lyapunov function, while the second divides it based on the change in the vector field of the PWA dynamical system. In addition, we propose using Delaunay triangulation to achieve automated division of regions and preserve the continuity of the PWA Lyapunov function. Examples involving learned models and explicit MPC controllers demonstrate that the proposed method of dividing regions leads to valid Lyapunov functions with fewer regions than existing methods, reducing the computational time taken for stability analysisComment: 11 pages, 11 figure

On the Impact of Gravity Compensation on Reinforcement Learning in Goal-Reaching Tasks for Robotic Manipulators

Advances in machine learning technologies in recent years have facilitated developments in autonomous robotic systems. Designing these autonomous systems typically requires manually specified models of the robotic system and world when using classical control-based strategies, or time consuming and computationally expensive data-driven training when using learning-based strategies. Combination of classical control and learning-based strategies may mitigate both requirements. However, the performance of the combined control system is not obvious given that there are two separate controllers. This paper focuses on one such combination, which uses gravity-compensation together with reinforcement learning (RL). We present a study of the effects of gravity compensation on the performance of two reinforcement learning algorithms when solving reaching tasks using a simulated seven-degree-of-freedom robotic arm. The results of our study demonstrate that gravity compensation coupled with RL can reduce the training required in reaching tasks involving elevated target locations, but not all target locations

Correct-by-construction reach-avoid control of partially observable linear stochastic systems

We study feedback controller synthesis for reach-avoid control of discrete-time, linear time-invariant (LTI) systems with Gaussian process and measurement noise. The problem is to compute a controller such that, with at least some required probability, the system reaches a desired goal state in finite time while avoiding unsafe states. Due to stochasticity and nonconvexity, this problem does not admit exact algorithmic or closed-form solutions in general. Our key contribution is a correct-by-construction controller synthesis scheme based on a finite-state abstraction of a Gaussian belief over the unmeasured state, obtained using a Kalman filter. We formalize this abstraction as a Markov decision process (MDP). To be robust against numerical imprecision in approximating transition probabilities, we use MDPs with intervals of transition probabilities. By construction, any policy on the abstraction can be refined into a piecewise linear feedback controller for the LTI system. We prove that the closed-loop LTI system under this controller satisfies the reach-avoid problem with at least the required probability. The numerical experiments show that our method is able to solve reach-avoid problems for systems with up to 6D state spaces, and with control input constraints that cannot be handled by methods such as the rapidly-exploring random belief trees (RRBT)

Sampling-Based Robust Control of Autonomous Systems with Non-Gaussian Noise

Controllers for autonomous systems that operate in safetycritical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise, and common assumptions are that the underlying distributions are known and/or Gaussian. In practice, however, these assumptions may be unrealistic and can lead to poor approximations of the true noise distribution. We present a novel planning method that does not rely on any explicit representation of the noise distributions. In particular, we address the problem of computing a controller that provides probabilistic guarantees on safely reaching a target. First, we abstract the continuous system into a discrete-state model that captures noise by probabilistic transitions between states. As a key contribution, we adapt tools from the scenario approach to compute probably approximately correct (PAC) bounds on these transition probabilities, based on a finite number of samples of the noise. We capture these bounds in the transition probability intervals of a socalled interval Markov decision process (iMDP). This iMDP is robust against uncertainty in the transition probabilities, and the tightness of the probability intervals can be controlled through the number of samples. We use state-of-the-art verification techniques to provide guarantees on the iMDP, and compute a controller for which these guarantees carry over to the autonomous system. Realistic benchmarks show the practical applicability of our method, even when the iMDP has millions of states or transitions.</p

Robust Control for Dynamical Systems With Non-Gaussian Noise via Formal Abstractions

Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, and common assumptions are that the underlying distributions are known and/or Gaussian. In practice, however, these assumptions may be unrealistic and can lead to poor approximations of the true noise distribution. We present a novel controller synthesis method that does not rely on any explicit representation of the noise distributions. In particular, we address the problem of computing a controller that provides probabilistic guarantees on safely reaching a target, while also avoiding unsafe regions of the state space. First, we abstract the continuous control system into a finite-state model that captures noise by probabilistic transitions between discrete states. As a key contribution, we adapt tools from the scenario approach to compute probably approximately correct (PAC) bounds on these transition probabilities, based on a finite number of samples of the noise. We capture these bounds in the transition probability intervals of a so-called interval Markov decision process (iMDP). This iMDP is, with a user-specified confidence probability, robust against uncertainty in the transition probabilities, and the tightness of the probability intervals can be controlled through the number of samples. We use state-of-the-art verification techniques to provide guarantees on the iMDP and compute a controller for which these guarantees carry over to the original control system. In addition, we develop a tailored computational scheme that reduces the complexity of the synthesis of these guarantees on the iMDP. Benchmarks on realistic control systems show the practical applicability of our method, even when the iMDP has hundreds of millions of transitions.Comment: To appear in the Journal of Artificial Intelligence Research (JAIR). arXiv admin note: text overlap with arXiv:2110.1266

Numerical Optimization of a Premixer for an Internal Combustion Engine using Producer Gas as a Fuel

269-275Gasification seems to be one of the sustainable green energy solutions to fulfill the current and future energy needs. For efficient utilization of producer gas on existing IC Engines, carburetor/premixer needs to be carefully designed and developed to achieve uniform mixing quality. A long radius nozzle type premixer has been designed for natural gas engine to be operated on producer gas as an alternate fuel. Different configurations of T – Type premixers with single air entry and twin air entry with different throat diameters and hole sizes are numerically analysed using ANSYS® CFX. Turbulence is modelled using RNG k - ε closure model. Mixer performance is compared in terms of constituents’ mass fraction, flow Uniformity Index (UI) and pressure penalty. Numerical analysis reveals that throat diameter, air entry type and air hole diameter governs mixing and pressure drop. Out of all configurations, twin air entry type premixer provides better mixing of producer gas and air. The optimized design of premixer shows that the absolute deviation in mass fraction of individual constituent lies in the range of ± 1.73% with respect to the actual mass fractions obtained. The average absolute deviation calculated is 1.37% with Uniformity Index 0.958 at the exit plane while the pressure drop across the premixer is 951 Pa

Prognostic model to predict postoperative acute kidney injury in patients undergoing major gastrointestinal surgery based on a national prospective observational cohort study.

Background: Acute illness, existing co-morbidities and surgical stress response can all contribute to postoperative acute kidney injury (AKI) in patients undergoing major gastrointestinal surgery. The aim of this study was prospectively to develop a pragmatic prognostic model to stratify patients according to risk of developing AKI after major gastrointestinal surgery. Methods: This prospective multicentre cohort study included consecutive adults undergoing elective or emergency gastrointestinal resection, liver resection or stoma reversal in 2-week blocks over a continuous 3-month period. The primary outcome was the rate of AKI within 7 days of surgery. Bootstrap stability was used to select clinically plausible risk factors into the model. Internal model validation was carried out by bootstrap validation. Results: A total of 4544 patients were included across 173 centres in the UK and Ireland. The overall rate of AKI was 14·2 per cent (646 of 4544) and the 30-day mortality rate was 1·8 per cent (84 of 4544). Stage 1 AKI was significantly associated with 30-day mortality (unadjusted odds ratio 7·61, 95 per cent c.i. 4·49 to 12·90; P < 0·001), with increasing odds of death with each AKI stage. Six variables were selected for inclusion in the prognostic model: age, sex, ASA grade, preoperative estimated glomerular filtration rate, planned open surgery and preoperative use of either an angiotensin-converting enzyme inhibitor or an angiotensin receptor blocker. Internal validation demonstrated good model discrimination (c-statistic 0·65). Discussion: Following major gastrointestinal surgery, AKI occurred in one in seven patients. This preoperative prognostic model identified patients at high risk of postoperative AKI. Validation in an independent data set is required to ensure generalizability

The impact of immediate breast reconstruction on the time to delivery of adjuvant therapy: the iBRA-2 study

Background: Immediate breast reconstruction (IBR) is routinely offered to improve quality-of-life for women requiring mastectomy, but there are concerns that more complex surgery may delay adjuvant oncological treatments and compromise long-term outcomes. High-quality evidence is lacking. The iBRA-2 study aimed to investigate the impact of IBR on time to adjuvant therapy. Methods: Consecutive women undergoing mastectomy ± IBR for breast cancer July–December, 2016 were included. Patient demographics, operative, oncological and complication data were collected. Time from last definitive cancer surgery to first adjuvant treatment for patients undergoing mastectomy ± IBR were compared and risk factors associated with delays explored. Results: A total of 2540 patients were recruited from 76 centres; 1008 (39.7%) underwent IBR (implant-only [n = 675, 26.6%]; pedicled flaps [n = 105,4.1%] and free-flaps [n = 228, 8.9%]). Complications requiring re-admission or re-operation were significantly more common in patients undergoing IBR than those receiving mastectomy. Adjuvant chemotherapy or radiotherapy was required by 1235 (48.6%) patients. No clinically significant differences were seen in time to adjuvant therapy between patient groups but major complications irrespective of surgery received were significantly associated with treatment delays. Conclusions: IBR does not result in clinically significant delays to adjuvant therapy, but post-operative complications are associated with treatment delays. Strategies to minimise complications, including careful patient selection, are required to improve outcomes for patients