Continuity and Monotonicity of the MPC Value Function with respect to Sampling Time and Prediction Horizon

The digital implementation of model predictive control (MPC) is fundamentally governed by two design parameters; sampling time and prediction horizon. Knowledge of the properties of the value function with respect to the parameters can be used for developing optimisation tools to find optimal system designs. In particular, these properties are continuity and monotonicity. This paper presents analytical results to reveal the smoothness properties of the MPC value function in open- and closed-loop for constrained linear systems. Continuity of the value function and its differentiability for a given number of prediction steps are proven mathematically and confirmed with numerical results. Non-monotonicity is shown from the ensuing numerical investigation. It is shown that increasing sampling rate and/or prediction horizon does not always lead to an improved closedloop performance, particularly at faster sampling rates

Analytical results for the multi-objective design of model-predictive control

In model-predictive control (MPC), achieving the best closed-loop performance under a given computational resource is the underlying design consideration. This paper analyzes the MPC design problem with control performance and required computational resource as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational resource separately -- often with the latter as a fixed constraint -- which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient solver are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the design approach and importance of the developed conditions for an effective solver of the MOD-MPC problem

What Is the Most Effective Management of the Primary Tumor in Men with Invasive Penile Cancer: A Systematic Review of the Available Treatment Options and Their Outcomes.

CONTEXT: The primary lesion in penile cancer is managed by surgery or radiation. Surgical options include penile-sparing surgery, amputative surgery, laser excision, and Moh's micrographic surgery. Radiation is applied as external beam radiotherapy (EBRT) and brachytherapy. The treatment aims to completely remove the primary lesion and preserve a sufficient functional penile stump. OBJECTIVE: To assess whether the 5-yr recurrence-free rate and other outcomes, such as sexual function, quality of life, urination, and penile preserving length, vary between various treatment options. EVIDENCE ACQUISITION: The EMBASE, MEDLINE, Cochrane Database of Systematic Reviews, Cochrane Central Register of Controlled Trials (CENTRAL; Cochrane HTA, DARE, HEED), Google Scholar, and ClinicalTrials.gov were searched for publications from 1990 through May 2021. Randomized controlled trials, nonrandomized comparative studies (NRCSs), and case series (CSs) were included. EVIDENCE SYNTHESIS: The systematic review included 88 studies, involving 9578 men from 16 NRCSs and 72 CSs. The cumulative mean 5-yr recurrence-free rates were 82.0% for penile-sparing surgery, 83.9% for amputative surgery, 78.6% for brachytherapy, 55.2% for EBRT, 69.4% for lasers, and 88.2% for Moh's micrographic surgery, as reported from CSs, and 76.7% for penile-sparing surgery and 93.3% for amputative surgery, as reported from NRCSs. Penile surgery affects sexual function, but amputative surgery causes more appearance concerns. After brachytherapy, 25% of patients reported sexual dysfunction. Both penile-sparing surgery and amputative surgery affect all aspects of psychosocial well-being. CONCLUSIONS: Despite the poor quality of evidence, data suggest that penile-sparing surgery is not inferior to amputative surgery in terms of recurrence rates in selected patients. Based on the available information, however, broadly applicable recommendations cannot be made; appropriate patient selection accounts for the relative success of all the available methods. PATIENT SUMMARY: We reviewed the evidence of various techniques to treat penile tumor and assessed their effectiveness in oncologic control and their functional outcomes. Penile-sparing as well as amputative surgery is an effective treatment option, but amputative surgery has a negative impact on sexual function. Penile-sparing surgery and radiotherapy are associated with a higher risk of local recurrence, but preserve sexual function and quality of life better. Laser and Moh's micrographic surgery could be used for smaller lesions

Management of Lymph Node-positive Penile Cancer: A Systematic Review.

CONTEXT: Lymph node (LN) involvement in penile cancer is associated with poor survival. Early diagnosis and management significantly impact survival, with multimodal treatment approaches often considered in advanced disease. OBJECTIVE: To assess the clinical effectiveness of treatment options available for the management of inguinal and pelvic lymphadenopathy in men with penile cancer. EVIDENCE ACQUISITION: EMBASE, MEDLINE, the Cochrane Database of Systematic Reviews, and other databases were searched from 1990 to July 2022. Randomised controlled trials (RCTs), nonrandomised comparative studies (NRCSs), and case series (CSs) were included. EVIDENCE SYNTHESIS: We identified 107 studies, involving 9582 patients from two RCTs, 28 NRCSs, and 77 CSs. The quality of evidence is considered poor. Surgery is the mainstay of LN disease management, with early inguinal LN dissection (ILND) associated with better outcomes. Videoendoscopic ILND may offer comparable survival outcomes to open ILND with lower wound-related morbidity. Ipsilateral pelvic LN dissection (PLND) in N2-3 cases improves overall survival in comparison to no pelvic surgery. Neoadjuvant chemotherapy in N2-3 disease showed a pathological complete response rate of 13% and an objective response rate of 51%. Adjuvant radiotherapy may benefit pN2-3 but not pN1 disease. Adjuvant chemoradiotherapy may provide a small survival benefit in N3 disease. Adjuvant radiotherapy and chemotherapy improve outcomes after PLND for pelvic LN metastases. CONCLUSIONS: Early LND improves survival in nodal disease in penile cancer. Multimodal treatments may provide additional benefit in pN2-3 cases; however, data are limited. Therefore, individualised management of patients with nodal disease should be discussed in a multidisciplinary team setting. PATIENT SUMMARY: Spread of penile cancer to the lymph nodes is best managed with surgery, which improves survival and has curative potential. Supplementary treatment, including the use of chemotherapy and/or radiotherapy, may further improve survival in advanced disease. Patients with penile cancer with lymph node involvement should be treated by a multidisciplinary team

Optimization Framework for Codesign of Controlled Aerodynamic Systems

Optimization studies of dynamic systems using high-fidelity numerical models necessitate a tradeoff between fidelity and the total computational time required during design. A gradient-based optimization framework is proposed for the aerodynamic shape and controller design of aerodynamic systems using computationally intensive high-fidelity models. Subject to some general properties, the framework offers flexibility in the types of simulation models used and provides guarantees regarding closeness to an optimal design. A nested optimization loop that allows for the partitioning of controller and plant architecture is implemented. The proposed framework exploits time-scale properties of the dynamic system model, closeness properties of partially converged iterative solutions of computational fluid dynamics models, and the continuous adjoint method. It is shown that combining these methods can improve the total computational time relative to finite differencing. An example of optimizing the aerodynamic body and control gains of a tail-fin controlled supersonic missile is presented

Near-time-optimal tracking controller design for an automotive electromechanical brake

C1 - Journal Articles RefereedA state-constrained, robust near-time-optimal clamp force tracking controller for an automotive electromechanical brake is presented. The proposed hybrid control structure consists of two switching control laws that handle tracking of rate-bounded references in the presence of state constraints. The responsive tracking utilizes an approximated time-optimal switching curve as a sliding manifold, while state constraints are handled by a linearizing–stabilizing feedback controller. The hybrid controller is proven to asymptotically track the reference in the presence of unknown but bounded time-varying disturbances and modelling errors. Implementation and validation of the proposed controller on a prototype electromechanical brake enables favourable performance comparisons with existing servo control architectures to be obtained

Robustness analysis of nonlinear observers for the slow variables of singularly perturbed systems

Estimation of unmeasured variables is a crucial objective in a broad range of applications. However, the estimation process turns into a challenging problem when the underlying model is nonlinear and even more so when additionally it exhibits multiple time scales. The existing results on estimation for systems with two time scales apply to a limited class of nonlinear plants and observers. We focus on analyzing nonlinear observers designed for the slow state variables of nonlinear singularly perturbed systems. Moreover, we consider the presence of bounded measurement noise in the system. We generalize current results by considering broader classes of plants and estimators to cover reduced-order, full-order, and higher-order observers. First, we show that the singularly perturbed system has bounded solutions under an appropriate set of assumptions on the corresponding boundary layer and reduced systems. We then exploit this property to prove that, under reasonable assumptions, the error dynamics of the observer designed for the reduced system are semiglobally input-to-state practically stable when the observer is implemented on the original plant. We also conclude (Formula presented.) stability results when the measurement noise belongs to (Formula presented.). In the absence of measurement noise, we state results on semiglobal practical asymptotical stability for the error dynamics. We illustrate the generality of our main results through three classes of systems with corresponding observers and one numerical example

Model reduction of automotive engines using perturbation theory

In this paper, a new constructive and versatile procedure to systematically reduce the order of control oriented engine models is presented. The technique is governed by the identification of time scale separation within the dynamics of various engine state variables and hence makes extensive use of the perturbation theory. On the basis of the dynamic characteristics and the geometry of engines, two methods for model reduction are proposed. Method 1 involves collective use of the regular and singular perturbation theories to eliminate temperature dynamics and approximate them with their quasi-steady state values, while Method 2 deals with the elimination of fast pressures. The result is a library of engine models which are associated with each other on a sound theoretical basis and simultaneously allow sufficient flexibility in terms of the reduced order modeling of a variety of engines. Different assumptions under which this model reduction is justified are presented and their implications are discussed