Hadi Ravanbakhsh

A model-based approach to synthesizing insulin infusion pump usage parameters for diabetic patients

We present a model-based approach to synthesizing insulin infusion pump usage parameters against varying meal scenarios and physiological conditions. Insulin infusion pumps are commonly used by type-1 diabetic patients to control their blood glucose levels. The amounts of insulin to be infused are calculated based on parameters such as insulin-to-carbohydrate ratios and correction factors that need to be calibrated carefully for each patient. Frequent and careful calibration of these parameters is essential for avoiding complications such as hypoglycemia and hyperglycemia. In this paper, we propose to synthesize optimal parameters for meal bolus calculation starting from models of the patients insulin-glucose regulatory system and the infusion pump. Various off-the-shelf global optimization techniques are used to search for parameter values that minimize a penalty function defined over the predicted glucose sensor readings. The penalty function “rewards” glucose levels that lie within the prescribed ranges and “penalizes” the occurrence of hypoglycemia and hyperglycemia. We evaluate our approach using a model of the insulin-glucose regulatory system proposed by Dalla Man et al. Using this model, we compare various strategies for optimizing pump usage parameters for a virtual population of in-silico patients.

Counter-Example Guided Synthesis of control Lyapunov functions for switched systems

We investigate the problem of synthesizing switching controllers for stabilizing continuous-time plants. First, we introduce a class of control Lyapunov functions (CLFs) for switched systems along with a switching strategy that yields a closed loop system with a guaranteed minimum dwell time in each switching mode. However, the challenge lies in automatically synthesizing appropriate CLFs. Assuming a given fixed form for the CLF with unknown coefficients, we derive quantified nonlinear constraints whose feasible solutions (if any) correspond to CLFs for the original system. However, solving quantified nonlinear constraints pose a challenge to most LMI/BMI-based relaxations. Therefore, we investigate a general approach called Counter-Example Guided Inductive Synthesis (CEGIS), that has been widely used in the emerging area of automatic program synthesis. We show how a LMI-based relaxation can be formulated within the CEGIS framework for synthesizing CLFs. We also evaluate our approach on a number of interesting benchmarks, and compare the performance of the new approach with our previous work that uses off-the-shelf nonlinear constraint solvers instead of the LMI relaxation. The results shows synthesizing CLFs by using LMI solvers inside a CEGIS framework can be a computational feasible approach to synthesizing CLFs.

Robust controller synthesis of switched systems using counterexample guided framework

We investigate the problem of synthesizing robust controllers that ensure that the closed loop satisfies an input reach-while-stay specification, wherein all trajectories starting from some initial set I, eventually reach a specified goal set G, while staying inside a safe set S. Our plant model consists of a continuous-time switched system controlled by an external switching signal and plant disturbance inputs. The controller uses a state feedback law to control the switching signal in order to ensure that the desired correctness properties hold, regardless of the disturbance actions. Our approach uses a proof certificate in the form of a robust control Lyapunov-like function (RCLF) whose existence guarantees the reach-while-stay specification. A counterexample guided inductive synthesis (CEGIS) framework is used to find a RCLF by solving a formula iteratively using quantifier free SMT solvers. We compare our synthesis scheme against a common approach that fixes disturbances to nominal values and synthesizes the controller, ignoring the disturbance. We demonstrate that the latter approach fails to yield a robust controller over some benchmark examples, whereas our approach does. Finally, we consider the problem of translating the RCLF synthesized by our approach into a control implementation. We outline the series of offline and real-time computation steps needed. The synthesized controller is implemented and simulated using the Matlab(tm)/Simulink(tm) model-based design framework, and illustrated on some examples.

Infinite horizon safety controller synthesis through disjunctive polyhedral abstract interpretation

This paper presents a controller synthesis approach using disjunctive polyhedral abstract interpretation. Our approach synthesizes infinite time-horizon controllers for safety properties with discrete-time, linear plant model and a switching feedback controller that is suitable for time-triggered implementations. The core idea behind our approach is to perform an abstract interpretation over disjunctions of convex polyhedra to identify states that are potentially uncontrollable. Complementing this set yields the set of controllable states, starting from which, the safety property can be guaranteed by an appropriate controller feedback function. Since, a straightforward disjunctive domain is computationally inefficient, we present an abstract domain based on a state partitioning scheme that allows us to efficiently control the complexity of the intermediate representations. Next, we focus on the automatic generation of controller implementation from the abstract interpretation results. We show that a balanced tree approach can yield efficient controller code with guarantees on the worst-case execution time. Finally, we evaluate our approach on a suite of benchmarks, comparing different instantiations with related synthesis tools. The evaluation shows that our approach can successfully synthesize controller implementations for small to medium sized benchmarks.

Learning Lyapunov (Potential) Functions from Counterexamples and Demonstrations.

We present a technique for learning control Lyapunov (potential) functions, which are used in turn to synthesize controllers for nonlinear dynamical systems. The learning framework uses a demonstrator that implements a black-box, untrusted strategy presumed to solve the problem of interest, a learner that poses finitely many queries to the demonstrator to infer a candidate function and a verifier that checks whether the current candidate is a valid control Lyapunov function. The overall learning framework is iterative, eliminating a set of candidates on each iteration using the counterexamples discovered by the verifier and the demonstrations over these counterexamples. We prove its convergence using ellipsoidal approximation techniques from convex optimization. We also implement this scheme using nonlinear MPC controllers to serve as demonstrators for a set of state and trajectory stabilization problems for nonlinear dynamical systems. Our approach is able to synthesize relatively simple polynomial control Lyapunov functions, and in that process replace the MPC using a guaranteed and computationally less expensive controller.

Learning control lyapunov functions from counterexamples and demonstrations

We present a technique for learning control Lyapunov-like functions, which are used in turn to synthesize controllers for nonlinear dynamical systems that can stabilize the system, or satisfy specifications such as remaining inside a safe set, or eventually reaching a target set while remaining inside a safe set. The learning framework uses a demonstrator that implements a black-box, untrusted strategy presumed to solve the problem of interest, a learner that poses finitely many queries to the demonstrator to infer a candidate function, and a verifier that checks whether the current candidate is a valid control Lyapunov-like function. The overall learning framework is iterative, eliminating a set of candidates on each iteration using the counterexamples discovered by the verifier and the demonstrations over these counterexamples. We prove its convergence using ellipsoidal approximation techniques from convex optimization. We also implement this scheme using nonlinear MPC controllers to serve as demonstrators for a set of state and trajectory stabilization problems for nonlinear dynamical systems. We show how the verifier can be constructed efficiently using convex relaxations of the verification problem for polynomial systems to semi-definite programming problem instances. Our approach is able to synthesize relatively simple polynomial control Lyapunov-like functions, and in that process replace the MPC using a guaranteed and computationally less expensive controller.

Affix-augmented stem-based language model for persian

Language modeling is used in many NLP applications like machine translation, POS tagging, speech recognition and information retrieval. It assigns a probability to a sequence of words. This task becomes a challenging problem for high inflectional languages. In this paper we investigate standard statistical language models on the Persian as an inflectional language. We propose two variations of morphological language models that rely on a morphological analyzer to manipulate the dataset before modeling. Then we discuss shortcoming of these models, and introduce a novel approach that exploits the structure of the language and produces more accurate. Experimental results are encouraging especially when we use n-gram models with small training dataset.

A Class of Control Certificates to Ensure Reach-While-Stay for Switched Systems.

In this article, we consider the problem of synthesizing switching controllers for temporal properties through the composition of simple primitive reach-while-stay (RWS) properties. Reach-while-stay properties specify that the system states starting from an initial set I, must reach a goal (target) set G in finite time, while remaining inside a safe set S. Our approach synthesizes switched controllers that select between finitely many modes to satisfy the given RWS specification. To do so, we consider control certificates, which are Lyapunov-like functions that represent control strategies to achieve the desired specification. However, for RWS problems, a control Lyapunov-like function is often hard to synthesize in a simple polynomial form. Therefore, we combine control barrier and Lyapunov functions with an additional compatibility condition between them. Using this approach, the controller synthesis problem reduces to one of solving quantified nonlinear constrained problems that are handled using a combination of SMT solvers. The synthesis of controllers is demonstrated through a set of interesting numerical examples drawn from the related work, and compared with the state-of-the-art tool SCOTS. Our evaluation suggests that our approach is computationally feasible, and adds to the growing body of formal approaches to controller synthesis.

Counterexample-guided stabilization of switched systems using control lyapunov functions

In this project, we address the problem of synthesizing region-stabilizing controllers for switched systems. The plant model consists of a continuous-time switched system with finitely many switching modes. Our approach searches for a state-feedback that chooses between finitely many switching modes at each time instant: (a) guaranteeing a minimum dwell time between mode changes and (b) region stabilizing to a suitably small set around a given state. First, we introduce a special class of control Lyapunov functions (CLF) for switched systems that yield switching controllers with a guaranteed minimum dwell time in each mode. After formulating the problem of finding such CLF as quantified exists-forall constraints, we employ a counter-example based inductive synthesis (CEGIS) approach to find a CLF with a given fixed template. We introduce a heuristic to increase the rate of convergence of the technique along with a relaxation to guarantee its eventual termination. We evaluate our approach on a set of benchmarks ranging from two to five state variables and compare the results with some of the existing approaches.