Computationally efficient solution of mixed integer model predictive control problems via machine learning aided Benders Decomposition

Mixed integer Model Predictive Control (MPC) problems arise in the operation of systems where discrete and continuous decisions must be taken simultaneously to compensate for disturbances. The efficient solution of mixed integer MPC problems requires the computationally efficient and robust online solution of mixed integer optimization problems, which are generally difficult to solve. In this paper, we propose a machine learning-based branch and check Generalized Benders Decomposition algorithm for the efficient solution of such problems. We use machine learning to approximate the effect of the complicating variables on the subproblem by approximating the Benders cuts without solving the subproblem, therefore, alleviating the need to solve the subproblem multiple times. The proposed approach is applied to a mixed integer economic MPC case study on the operation of chemical processes. We show that the proposed algorithm always finds feasible solutions to the optimization problem, given that the mixed integer MPC problem is feasible, and leads to a significant reduction in solution time (up to 97% or 50x) while incurring small error (in the order of 1%) compared to the application of standard and accelerated Generalized Benders Decomposition

Synthesis of feedforward/state feedback controllers for nonlinear processes

A systematic method for synthesizing feedforward/state feedback controllers for a broad class of SISO nonlinear systems with measurable disturbances is presented. Depending on the structural characteristics of the system, the control law can be static or dynamic. The closed-loop system is independent of the measurable disturbances and linear with respect to set point changes. The performance of the proposed control scheme is illustrated through an example of composition control in a system of three CSTR's in series.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/37404/1/690351004_ftp.pd

Dynamic output feedback control of minimum-phase multivariable nonlinear processes

This paper concerns the synthesis of dynamic output feedback controllers for minimum-phase multivariable nonlinear processes with a nonsingular characteristic matrix. State-space controller realizations are derived that induce a linear input/output behavior of general form in the closed-loop system. A combination of input/output linearizing state feedback laws and state observers is employed for the derivation of the controllers. For open-loop stable processes, the process model is used as an open-loop state observer. In the more general case of possible open-loop instability, a reduced-order observer is used based on the forced zero dynamics of the process model. The performance and robustness characteristics of the proposed control methodology are illustrated through simulations in a chemical reactor example.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31933/1/0000886.pd

Inversion and zero dynamics in nonlinear multivariable control

This work concerns general multiple-input/multiple-output (MIMO) nonlinear systems with nonsingular characteristic matrix. For these systems, the problem of inversion is revisited and explicit formulas are derived for the full-order and the reduced inverse system. The reduced inverse naturally leads to an explicit calculation of the unforced zero dynamics of the system and the definition of a concept of forced zero dynamics. These concepts generalize the notion of transmission zeros for MIMO linear systems in a nonlinear setting. Chemical engineering examples are given to illustrate the calculation of zero dynamics. Input/output linearization is then interpreted as canceling the forced zero dynamics of the system, and precise internal stability conditions are derived for the closed-loop system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/37419/1/690370406_ftp.pd

Stochastic simulations of the tetracycline operon

<p>Abstract</p> <p>Background</p> <p>The tetracycline operon is a self-regulated system. It is found naturally in bacteria where it confers resistance to antibiotic tetracycline. Because of the performance of the molecular elements of the tetracycline operon, these elements are widely used as parts of synthetic gene networks where the protein production can be efficiently turned on and off in response to the presence or the absence of tetracycline. In this paper, we investigate the dynamics of the tetracycline operon. To this end, we develop a mathematical model guided by experimental findings. Our model consists of biochemical reactions that capture the biomolecular interactions of this intriguing system. Having in mind that small biological systems are subjects to stochasticity, we use a stochastic algorithm to simulate the tetracycline operon behavior. A sensitivity analysis of two critical parameters embodied this system is also performed providing a useful understanding of the function of this system.</p> <p>Results</p> <p>Simulations generate a timeline of biomolecular events that confer resistance to bacteria against tetracycline. We monitor the amounts of intracellular TetR2 and TetA proteins, the two important regulatory and resistance molecules, as a function of intrecellular tetracycline. We find that lack of one of the promoters of the tetracycline operon has no influence on the total behavior of this system inferring that this promoter is not essential for <it>Escherichia coli</it>. Sensitivity analysis with respect to the binding strength of tetracycline to repressor and of repressor to operators suggests that these two parameters play a predominant role in the behavior of the system. The results of the simulations agree well with experimental observations such as tight repression, fast gene expression, induction with tetracycline, and small intracellular TetR2 amounts.</p> <p>Conclusions</p> <p>Computer simulations of the tetracycline operon afford augmented insight into the interplay between its molecular components. They provide useful explanations of how the components and their interactions have evolved to best serve bacteria carrying this operon. Therefore, simulations may assist in designing novel gene network architectures consisting of tetracycline operon components.</p

Nonlinear state feedback control of second-order nonminimum-phase nonlinear systems

The present work addresses the problem of synthesizing nonlinear state feedback controllers for second-order nonminimum-phase nonlinear systems. The concept of a first-order nonlinear all-pass is first introduced. A class of static state feedback control laws is then developed that makes the closed-loop system equivalent, under an appropriate coordinate transformation, to a nonlinear first-order all-pass in series with a linear first-order lag. A particular control law from this class is calculated that results in ISE-optimal response. The performance of the proposed methodology in set point tracking is evaluated through numerical simulations in a CSTR example.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28607/1/0000416.pd

Feedforward/feedback control of multivariable nonlinear processes

This paper concerns general MIMO nonlinear processes, whose dynamic behavior is described by a standard state-space model of arbitrary order, including measurable disturbances. The concept of relative order of an output with respect to an input, extended to include disturbance as well as manipulated inputs, is generalized in a MIMO context and it is used to obtain a characterization of the dynamic interactions among the input and the output variables. A synthesis formula is calculated for a feedforward/state feedback control law that completely eliminates the effect of the measurable disturbances on the process outputs and induces a linear behavior in the closed-loop system between the outputs and a set of reference inputs. The input/output stability and the degree of coupling in the closed-loop system are determined by appropriate choice of adjustable parameters. A MIMO linear controller with integral action completes the feedforward/feedback control structure. The developed control methodology is applied to a continuous polymerization reactor and its performance is evaluated through simulations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/37411/1/690361003_ftp.pd

Metabolic pathway engineering in mammalian cells through kinetic model optimization

Excessive lactate production and accumulation in cell culture can result in reduced culture productivity and altered product quality. Engineering cell metabolism to eliminate or reduce lactate production can lead to higher performing, more robust processes. However, prior efforts to engineer cell lines with low lactate production have been met with limited success, often also resulting in reduced cell growth rate. Given the complex roles of energy metabolism in sustaining anabolism and redox homeostasis, it is likely that successful suppression of lactate production in proliferating cells will require simultaneous alteration of multiple genes in energy metabolism. Considering the nonlinear nature of the energy metabolism reactions and the number of reactions involved, we have taken a systems approach to devise a strategy to alter cellular metabolic behavior to advance cell culture bioprocessing. In this study, we develop a method using optimization of a nonlinear kinetic model of cell metabolism designed to rewire glycolysis to have reduced lactate production while maintaining a high growth rate. The model encompasses glycolysis, the pentose phosphate pathway, and the citric acid cycle, and also includes the known allosteric regulations. The large number of possible enzyme combinations necessitates a method to search the parameter space intelligently for key changes that can be made to manipulate metabolism. The model was solved using a local nonlinear optimizer embedded in General Algebraic Modeling System (GAMS). A multi-objective optimization was formulated, demonstrating the relationship between lactate production and glucose consumption. Constraints were chosen to maintain cellular requirements for growth including energy production and precursors for biosynthesis. The primary objective of this optimization was to minimize the rate of lactate production for cells in culture, but the objective function was modified with a penalty term to also reduce the number of genetic alterations in an optimal state to ease experimental design. The resulting solutions to the optimization problem contain small sets of recommended changes to enzyme expression and activity that can be tested in an engineered cell line. We have demonstrated a method for rationally guiding cellular engineering through kinetic model optimization. The findings from this optimization are being evaluated experimentally, generating new cell lines with altered metabolic behavior. By identifying sets of parameter changes that yield desirable outcomes, optimization of kinetic models can greatly reduce the effort required to engineer cell metabolism, providing multiple metabolic engineering strategies with different enzyme combinations as well as deep insight into the reaction networks and their behavior

Output feedback control of nonminimum-phase nonlinear processes

This work concerns the development of a general framework for the analysis and output feedback control of open-loop stable nonminimum-phase nonlinear processes. A Smith-type abstract operator structure is introduced, allowing the reduction of the controller synthesis problem for nonminimum-phase processes to the one for minimum-phase processes. State-space methods are used to derive a reduced-order output feedback controller that induces a desired input/output behavior for processes with unstable inverse dynamics and deadtime. The underlying structure of the reduced-order controller is also identified and studied. Finally, an example from a class of chemical reaction systems with nonminimum-phase characteristics is used for evaluating the performance and robustness of the developed control method.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31490/1/0000412.pd